To simplify the expression 2^4 ⋅ 2^2 using the Product Rule of Exponents, we add the exponents when multiplying two numbers with the same base.
2^4 ⋅ 2^2 = 2^(4+2) = 2^6
Therefore, the simplified expression is 2^6.
Use the Product Rule of Exponents to simplify the expression 2^4 ⋅2^2.
69 answers
Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
(5^2) 9
10^8⋅10^8
32^7
6^2⋅7^3
Responses
(5^2) 9
10^8⋅10^8
32^7
6^2⋅7^3
The expression that is correctly developed to use the Product Rule of Exponents is:
10^8 ⋅ 10^8
10^8 ⋅ 10^8
Simplify x^675/x^453
To simplify x^675 / x^453, we can use the quotient rule of exponents.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
So, x^675 / x^453 = x^(675-453) = x^222.
Therefore, the simplified expression is x^222.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
So, x^675 / x^453 = x^(675-453) = x^222.
Therefore, the simplified expression is x^222.
What is the missing exponent in the following equation?
e^?/e^65 = e^38
e^?/e^65 = e^38
To find the missing exponent in the equation e^?/e^65 = e^38, we can use the quotient rule of exponents.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
So, e^?/e^65 = e^(?-65) = e^38.
To solve for the missing exponent, we can set the exponents equal to each other:
?-65 = 38.
To isolate the missing exponent, we can add 65 to both sides:
?-65 + 65 = 38 + 65.
This simplifies to:
? = 103.
Therefore, the missing exponent in the equation is 103.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
So, e^?/e^65 = e^(?-65) = e^38.
To solve for the missing exponent, we can set the exponents equal to each other:
?-65 = 38.
To isolate the missing exponent, we can add 65 to both sides:
?-65 + 65 = 38 + 65.
This simplifies to:
? = 103.
Therefore, the missing exponent in the equation is 103.
Simplify 13^12÷13^−10
.
.
To simplify 13^12 ÷ 13^(-10), we can use the quotient rule of exponents.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
So, 13^12 ÷ 13^(-10) = 13^(12 - (-10)) = 13^(12 + 10) = 13^22.
Therefore, the simplified expression is 13^22.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
So, 13^12 ÷ 13^(-10) = 13^(12 - (-10)) = 13^(12 + 10) = 13^22.
Therefore, the simplified expression is 13^22.
Simplify 4^13÷3^−5
To simplify 4^13 ÷ 3^(-5), we can again use the quotient rule of exponents.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
So, 4^13 ÷ 3^(-5) = 4^13 * 3^5.
Now, we can simplify this further by expanding both terms:
4^13 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 67,108,864.
3^5 = 3 * 3 * 3 * 3 * 3 = 243.
Now, we can substitute these values back into the expression:
4^13 ÷ 3^(-5) = 67,108,864 ÷ 243 = 276,824.
Therefore, the simplified expression is 276,824.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
So, 4^13 ÷ 3^(-5) = 4^13 * 3^5.
Now, we can simplify this further by expanding both terms:
4^13 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 67,108,864.
3^5 = 3 * 3 * 3 * 3 * 3 = 243.
Now, we can substitute these values back into the expression:
4^13 ÷ 3^(-5) = 67,108,864 ÷ 243 = 276,824.
Therefore, the simplified expression is 276,824.
Simplify 4^13÷3^ −5
To simplify 4^13 ÷ 3^(-5), we can apply the negative exponent rule.
According to the negative exponent rule, any number raised to a negative exponent can be moved to the opposite side of the fraction with a positive exponent. So, 3^(-5) can be rewritten as 1/(3^5).
Now, we can rewrite the expression as: 4^13 ÷ (1/(3^5)).
To divide by a fraction, we can multiply by its reciprocal. So, we can rewrite the expression as: 4^13 * (3^5/1).
Now, we can apply the product rule of exponents which states that when multiplying two numbers with the same base, we add the exponents. So, we can add the exponents 13 and 5: 4^(13+5).
Simplifying further, 4^(13+5) = 4^18.
Therefore, the simplified expression is 4^18.
According to the negative exponent rule, any number raised to a negative exponent can be moved to the opposite side of the fraction with a positive exponent. So, 3^(-5) can be rewritten as 1/(3^5).
Now, we can rewrite the expression as: 4^13 ÷ (1/(3^5)).
To divide by a fraction, we can multiply by its reciprocal. So, we can rewrite the expression as: 4^13 * (3^5/1).
Now, we can apply the product rule of exponents which states that when multiplying two numbers with the same base, we add the exponents. So, we can add the exponents 13 and 5: 4^(13+5).
Simplifying further, 4^(13+5) = 4^18.
Therefore, the simplified expression is 4^18.
Simplify this expression using the Quotient Rule of Integer Exponents: t^400/t^100
Using the Quotient Rule of Integer Exponents, when dividing two numbers with the same base, we subtract the exponents.
So, t^400 / t^100 = t^(400-100) = t^300.
Therefore, the simplified expression is t^300.
So, t^400 / t^100 = t^(400-100) = t^300.
Therefore, the simplified expression is t^300.
Simplify a^67/b^34
To simplify a^67 / b^34, we can use the Quotient Rule of Exponents.
According to the Quotient Rule, when dividing two numbers with the same base, we subtract the exponents.
So, a^67 / b^34 = a^(67-34) / b^34 = a^33 / b^34.
Therefore, the simplified expression is a^33 / b^34.
According to the Quotient Rule, when dividing two numbers with the same base, we subtract the exponents.
So, a^67 / b^34 = a^(67-34) / b^34 = a^33 / b^34.
Therefore, the simplified expression is a^33 / b^34.
Apply the Quotient Rule of Integer Exponents to simplify 23^65÷23^32
To simplify 23^65 ÷ 23^32 using the Quotient Rule of Integer Exponents, we subtract the exponents when dividing two numbers with the same base.
So, 23^65 ÷ 23^32 = 23^(65 - 32) = 23^33.
Therefore, the simplified expression is 23^33.
So, 23^65 ÷ 23^32 = 23^(65 - 32) = 23^33.
Therefore, the simplified expression is 23^33.
Simplify this expression using the Quotient Rule of Integer Exponents: 12^53÷7^53
To simplify 12^53 ÷ 7^53 using the Quotient Rule of Integer Exponents, we subtract the exponents when dividing two numbers with the same base.
So, 12^53 ÷ 7^53 = (12/7)^53.
Therefore, the simplified expression is (12/7)^53.
So, 12^53 ÷ 7^53 = (12/7)^53.
Therefore, the simplified expression is (12/7)^53.
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?(1 point)
Responses
A. Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
B. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
C. Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
D. Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Responses
A. Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
B. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
C. Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
D. Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
The correct step to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents is:
B. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
B. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Simplify this expression using the Quotient Rule of Integer Exponents: 12^53÷7^53.
To simplify 12^53 ÷ 7^53 using the Quotient Rule of Integer Exponents, we subtract the exponents when dividing two numbers with the same base.
So, 12^53 ÷ 7^53 = (12/7)^53.
Therefore, the simplified expression is (12/7)^53.
So, 12^53 ÷ 7^53 = (12/7)^53.
Therefore, the simplified expression is (12/7)^53.
Apply the Zero Power Rule of Integer Exponents to solve 630.
To apply the Zero Power Rule of Integer Exponents, any non-zero number raised to the power of 0 is equal to 1.
Thus, 630^0 = 1.
Therefore, the solution is 1.
Thus, 630^0 = 1.
Therefore, the solution is 1.
Apply the Zero Power Rule of Integer Exponents to solve 63^0.
To apply the Zero Power Rule of Integer Exponents, any non-zero number raised to the power of 0 is equal to 1.
Thus, 63^0 = 1.
Therefore, the solution is 1.
Thus, 63^0 = 1.
Therefore, the solution is 1.
Apply the Zero Power Rule of Integer Exponents to solve −4^0⋅15.(1 point)
To apply the Zero Power Rule of Integer Exponents, any non-zero number raised to the power of 0 is equal to 1.
So, -4^0 * 15 = 1 * 15.
Therefore, the solution is 15.
So, -4^0 * 15 = 1 * 15.
Therefore, the solution is 15.
Apply the Zero Power Rule to create an equivalent expression to /43(−2+1^0).(1 point)
An equivalent expression to 4/3(−2+1^0) is 4/3(−2+?).
An equivalent expression to 4/3(−2+1^0) is 4/3(−2+?).
To apply the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1.
So, in the expression 4/3(-2+1^0), the term 1^0 can be simplified to 1.
Therefore, an equivalent expression would be 4/3(-2 + 1).
So, in the expression 4/3(-2+1^0), the term 1^0 can be simplified to 1.
Therefore, an equivalent expression would be 4/3(-2 + 1).
Solve the expression 2(1.6^0+7)−4.9^0.
To solve the expression 2(1.6^0 + 7) - 4.9^0, we can start by applying the Zero Power Rule.
According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1.
So, 1.6^0 = 1 and 4.9^0 = 1.
Therefore, the expression becomes 2(1 + 7) - 1 = 2(8) - 1 = 16 - 1 = 15.
So, the solution to the expression is 15.
According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1.
So, 1.6^0 = 1 and 4.9^0 = 1.
Therefore, the expression becomes 2(1 + 7) - 1 = 2(8) - 1 = 16 - 1 = 15.
So, the solution to the expression is 15.
Which of the following shows the correct process of solving −30+4.5?(1 point)
Responses
A. −3^0+4.5=−3⋅0+4.5=0+4.5=4.5
B. −3^0+4.5=−1⋅3^0+4.5=−1⋅1+4.5=−1+4.5=3.5
C. −3^0+4.5=(−3)^0+4.5=1+4.5=5.5
D. −3^0+4.5=−3+4.5=1.5
Responses
A. −3^0+4.5=−3⋅0+4.5=0+4.5=4.5
B. −3^0+4.5=−1⋅3^0+4.5=−1⋅1+4.5=−1+4.5=3.5
C. −3^0+4.5=(−3)^0+4.5=1+4.5=5.5
D. −3^0+4.5=−3+4.5=1.5
The correct process of solving −30+4.5 is as follows:
D. −3^0+4.5=−3+4.5=1.5
D. −3^0+4.5=−3+4.5=1.5
Which of the following is an equivalent expression to 7/(−5.3)^0+4⋅9 when applying the Zero Power Rule? (1 point)
Responses
A. 7/5.3+4⋅9
B. 7/5.3^0+36
C. 7/0+4⋅9
D. 7/1+4⋅9
Responses
A. 7/5.3+4⋅9
B. 7/5.3^0+36
C. 7/0+4⋅9
D. 7/1+4⋅9
To apply the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1.
The equivalent expression to 7/(−5.3)^0 + 4 * 9 would be:
D. 7/1 + 4 * 9
This is because any number raised to the power of 0 is equal to 1, and any number divided by 1 remains unchanged.
The equivalent expression to 7/(−5.3)^0 + 4 * 9 would be:
D. 7/1 + 4 * 9
This is because any number raised to the power of 0 is equal to 1, and any number divided by 1 remains unchanged.
solve −4(3+12^0)+15^0
To solve −4(3 + 12^0) + 15^0, we start by applying the Zero Power Rule.
According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1.
So, 12^0 = 1 and 15^0 = 1.
Now we can substitute these values back into the expression:
−4(3 + 1) + 1 = −4(4) + 1
Now we simplify inside the parentheses:
−16 + 1
Finally, we combine like terms:
−15
Therefore, the solution to the expression is −15.
According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1.
So, 12^0 = 1 and 15^0 = 1.
Now we can substitute these values back into the expression:
−4(3 + 1) + 1 = −4(4) + 1
Now we simplify inside the parentheses:
−16 + 1
Finally, we combine like terms:
−15
Therefore, the solution to the expression is −15.
solving −3^0+4.5?
To solve the expression −3^0 + 4.5, we first need to evaluate the exponent 0.
According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1.
So, −3^0 becomes −1.
Now we can substitute this value back into the expression:
−1 + 4.5
Finally, we sum up the terms:
3.5
Therefore, the solution to the expression is 3.5.
According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1.
So, −3^0 becomes −1.
Now we can substitute this value back into the expression:
−1 + 4.5
Finally, we sum up the terms:
3.5
Therefore, the solution to the expression is 3.5.
Use the Power Rule of Exponents to simplify the expression (6^2)^4
To simplify the expression (6^2)^4 using the Power Rule of Exponents, we multiply the exponents.
So, (6^2)^4 = 6^(2 * 4) = 6^8.
Therefore, the simplified expression is 6^8.
So, (6^2)^4 = 6^(2 * 4) = 6^8.
Therefore, the simplified expression is 6^8.
Use the Power Rule of Exponents to create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12).
To simplify the expression (12⋅12⋅12)⋅(12⋅12⋅12) using the Power Rule of Exponents, we can rewrite it as (12^3)⋅(12^3).
According to the Power Rule of Exponents, when raising a power to another power, we multiply the exponents.
So, (12^3)⋅(12^3) = 12^(3+3) = 12^6.
Therefore, a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12) would be 12^6.
According to the Power Rule of Exponents, when raising a power to another power, we multiply the exponents.
So, (12^3)⋅(12^3) = 12^(3+3) = 12^6.
Therefore, a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12) would be 12^6.
What exponent would make the two expressions equivalent: (16^x)^6=(16^18)?
To find the exponent that would make the two expressions equivalent, we can set the exponents equal to each other.
So, (16^x)^6 = 16^18.
According to the power rule of exponents, when raising an exponent to another exponent, we multiply the exponents.
Therefore, x * 6 = 18.
To solve for x, we divide both sides of the equation by 6:
x = 18/6.
Simplifying, we have:
x = 3.
Therefore, the exponent that would make the two expressions equivalent is x = 3.
So, (16^x)^6 = 16^18.
According to the power rule of exponents, when raising an exponent to another exponent, we multiply the exponents.
Therefore, x * 6 = 18.
To solve for x, we divide both sides of the equation by 6:
x = 18/6.
Simplifying, we have:
x = 3.
Therefore, the exponent that would make the two expressions equivalent is x = 3.
Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses
A. (7^4)^8
B. (−5)^0
C. 12^9
D. (7^8)⋅(7^10)
Responses
A. (7^4)^8
B. (−5)^0
C. 12^9
D. (7^8)⋅(7^10)
The expression that is correctly developed to use the Power Rule of Exponents is:
A. (7^4)^8
A. (7^4)^8
Which of the following correctly used the Power Rule of Exponents in the expression (109)7?(1 point)
Responses
A. 10^2
B. 10^63
C. 90^7
D. 10^16
Responses
A. 10^2
B. 10^63
C. 90^7
D. 10^16
The correct response is:
B. 10^63
This is the correct application of the Power Rule of Exponents, as raising 10 to the power of 7 (109) is equivalent to multiplying the exponents, resulting in 10^63.
B. 10^63
This is the correct application of the Power Rule of Exponents, as raising 10 to the power of 7 (109) is equivalent to multiplying the exponents, resulting in 10^63.
What exponent would make the two expressions equivalent: (3^3)^x=3^24?
To find the exponent that would make the two expressions equivalent, we can set the exponents equal to each other.
So, (3^3)^x = 3^24.
According to the power rule of exponents, when raising an exponent to another exponent, we multiply the exponents.
Therefore, 3^3x = 3^24.
To make the bases equal and set the exponents equal, we can equate the exponents:
3x = 24.
To solve for x, we divide both sides of the equation by 3:
x = 24/3.
Simplifying, we have:
x = 8.
Therefore, the exponent that would make the two expressions equivalent is x = 8.
So, (3^3)^x = 3^24.
According to the power rule of exponents, when raising an exponent to another exponent, we multiply the exponents.
Therefore, 3^3x = 3^24.
To make the bases equal and set the exponents equal, we can equate the exponents:
3x = 24.
To solve for x, we divide both sides of the equation by 3:
x = 24/3.
Simplifying, we have:
x = 8.
Therefore, the exponent that would make the two expressions equivalent is x = 8.
How do people in the Spanish-speaking world invite people to their parties?
(1 point)
Responses
Formal, written invitations
Posting the celebration in the newspaper well in advance
Verbally and without much notice
(1 point)
Responses
Formal, written invitations
Posting the celebration in the newspaper well in advance
Verbally and without much notice
The response is:
Verbally and without much notice
Verbally and without much notice
Which of the following is not true about Barcelona?
(1 point)
Responses
It is the capital of the Catalonian region of Spain.
It is the largest city in Spain.
It is home to the Tibidabo Amusement Park.
(1 point)
Responses
It is the capital of the Catalonian region of Spain.
It is the largest city in Spain.
It is home to the Tibidabo Amusement Park.
The response is:
It is the largest city in Spain.
It is the largest city in Spain.
In the Spanish-speaking world, what is Santos?
(1 point)
Responses
A fiesta much like a second-birthday
A common food to serve at parties
A park in Barcelona named for the saints
(1 point)
Responses
A fiesta much like a second-birthday
A common food to serve at parties
A park in Barcelona named for the saints
The correct response is:
A park in Barcelona named for the saints
A park in Barcelona named for the saints
What is the formal way to use the plural form for “you” in most of Spain?
(1 point)
Responses
ustedes
vosotros
vosotras
(1 point)
Responses
ustedes
vosotros
vosotras
The correct response is:
ustedes
ustedes
How do you say “fifteen” in Spanish?
(1 point)
Responses
catorce
quince
trece
(1 point)
Responses
catorce
quince
trece
The correct response is:
quince
quince
The following sentence comes from a birthday party invitation. What does it mean in English?
“Celebramos el cumpleaños . . . ”
(1 point)
Responses
“Meet at the park . . . ”
“Celebrate the birthday . . . ”
“Lots of presents . . . ”
"Please RSVP . . .
“Celebramos el cumpleaños . . . ”
(1 point)
Responses
“Meet at the park . . . ”
“Celebrate the birthday . . . ”
“Lots of presents . . . ”
"Please RSVP . . .
The correct response is:
“Celebrate the birthday . . . ”
“Celebrate the birthday . . . ”
Conduct a safe search of the Internet using the search terms "Federalist Papers" and "Anti-Federalist Papers" to find supporting evidence for your analysis. Include at least one direct quote from the Federalist Papers in your portfolio. Other research sources may be included, but are not required. If other sources are used, cite them using APA style.
Conduct a safe search of the Internet using the search terms "Federalist Papers" and "Anti-Federalist Papers" to find supporting evidence for your analysis. Include at least one direct quote from the Federalist Papers in your portfolio. Other research sources may be included, but are not required. If other sources are used, cite them using APA style.Conduct a safe search of the Internet using the search terms "Federalist Papers" and "Anti-Federalist Papers" to find supporting evidence for your analysis. Include at least one direct quote from the Federalist Papers in your portfolio. Other research sources may be included, but are not required. If other sources are used, cite them using APA style.
1 answer