To solve this expression, we need to follow the order of operations (also known as PEMDAS: Parentheses, Exponents, Multiplication and Division - from left to right, and Addition and Subtraction - from left to right).
First, let's solve the expression inside the parentheses: 7^0 = 1.
Now let's substitute that value back into the expression: 15⋅8^0/5 + 4(1−6).
Next, let's simplify the exponent: 8^0 = 1.
Now we have: 15⋅1/5 + 4(1−6).
Next, let's solve the expression inside the second set of parentheses: 1−6 = -5.
Now we have: 15⋅1/5 + 4(-5).
Next, let's multiply: 15⋅1 = 15.
Now we have: 15/5 + 4(-5).
Next, let's divide: 15/5 = 3.
Now we have: 3 + 4(-5).
Next, let's multiply: 4(-5) = -20.
Now we have: 3 + (-20).
Finally, let's add: 3 + (-20) = -17.
Therefore, the expression 15⋅8^0/5 + 4(7^0−6) equals -17.
Question
Solve the expression 1^5⋅8^0/5 + 4(7^0−6).(1 point)
15⋅8^0/5 + 4(7^0−6)=
27 answers
Use the Power Rule of Exponents to simplify (10^3)6 .(1 point)
To simplify the expression (10^3)^6 using the Power Rule of Exponents, we need to multiply the exponents together.
The Power Rule states that when you have a power of a power, you multiply the exponents.
In this case, we have (10^3)^6. We know that 10^3 means 10 multiplied by itself three times: 10 * 10 * 10 = 1,000.
So we can replace (10^3) with 1,000: 1,000^6.
To simplify this further, we need to multiply the exponents 6 and 3 together: 1,000^6 = (1,000)^(6 * 3) = 1,000^18.
Therefore, (10^3)^6 simplifies to 1,000^18.
The Power Rule states that when you have a power of a power, you multiply the exponents.
In this case, we have (10^3)^6. We know that 10^3 means 10 multiplied by itself three times: 10 * 10 * 10 = 1,000.
So we can replace (10^3) with 1,000: 1,000^6.
To simplify this further, we need to multiply the exponents 6 and 3 together: 1,000^6 = (1,000)^(6 * 3) = 1,000^18.
Therefore, (10^3)^6 simplifies to 1,000^18.
Use the Power Rule of Exponents to simplify (10^3)^6 .(1 point)
To simplify the expression (10^3)^6 using the Power Rule of Exponents, we need to multiply the exponents together.
The Power Rule states that when you have an exponent raised to another exponent, you multiply the exponents.
In this case, we have (10^3)^6. We can rewrite this as 10^(3*6).
So, 3*6 = 18.
Therefore, (10^3)^6 simplifies to 10^18.
The Power Rule states that when you have an exponent raised to another exponent, you multiply the exponents.
In this case, we have (10^3)^6. We can rewrite this as 10^(3*6).
So, 3*6 = 18.
Therefore, (10^3)^6 simplifies to 10^18.
If the expression 7^15 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)
Responses
(7^18)^3
(7^10)^5
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
(7⋅7⋅7⋅7⋅7)^10
Responses
(7^18)^3
(7^10)^5
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
(7⋅7⋅7⋅7⋅7)^10
If the expression 7^15 was simplified using the Power Rule of Exponents, the expanded equivalent expression would be (7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7).
This is because the Power Rule of Exponents states that when you multiply a number raised to a power multiple times, you multiply the exponents together.
In this case, 7^15 can be expanded as (7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7). Each group of three 7s is multiplied together, and we have a total of 15 7s being multiplied.
This is because the Power Rule of Exponents states that when you multiply a number raised to a power multiple times, you multiply the exponents together.
In this case, 7^15 can be expanded as (7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7). Each group of three 7s is multiplied together, and we have a total of 15 7s being multiplied.
Question
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9 .(1 point)
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9 .(1 point)
To simplify the expression (19^4)^9 using the Power Rule of Exponents, we need to multiply the exponents together.
The Power Rule states that when you have an exponent raised to another exponent, you multiply the exponents.
In this case, we have (19^4)^9. We can rewrite this as 19^(4*9).
So, 4*9 = 36.
Therefore, (19^4)^9 simplifies to 19^36.
The Power Rule states that when you have an exponent raised to another exponent, you multiply the exponents.
In this case, we have (19^4)^9. We can rewrite this as 19^(4*9).
So, 4*9 = 36.
Therefore, (19^4)^9 simplifies to 19^36.
Apply the Property of Negative Integer Exponents to solve 7^−3 . The answer should not contain any exponent expression or decimals.(1 point)
7^−3=
7^−3=
When applying the Property of Negative Integer Exponents, we can rewrite any number raised to a negative exponent as the reciprocal of the number raised to the positive exponent.
So, 7^(-3) becomes 1/(7^3).
Now, let's simplify 7^3: 7^3 = 7 * 7 * 7 = 343.
Therefore, 7^(-3) simplifies to 1/343.
So, 7^(-3) becomes 1/(7^3).
Now, let's simplify 7^3: 7^3 = 7 * 7 * 7 = 343.
Therefore, 7^(-3) simplifies to 1/343.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17/8^−14 with positive exponents only.(1 point)
3−^17/8^−14=
3−^17/8^−14=
To apply the Property of Negative Integer Exponents and generate an expression equivalent to 3^(-17)/8^(-14) with positive exponents only, we can rewrite it as:
(1/3^17)/(1/8^14)
By using the property of division, we can convert the division of fractions to multiplication of reciprocals:
(1/3^17)*(8^14/1)
Now, we can apply the property of negative exponents. When a fraction with a negative exponent is moved to the denominator, the exponent becomes positive:
(8^14)/(3^17)
Therefore, the expression equivalent to 3^(-17)/8^(-14) with positive exponents only is (8^14)/(3^17).
(1/3^17)/(1/8^14)
By using the property of division, we can convert the division of fractions to multiplication of reciprocals:
(1/3^17)*(8^14/1)
Now, we can apply the property of negative exponents. When a fraction with a negative exponent is moved to the denominator, the exponent becomes positive:
(8^14)/(3^17)
Therefore, the expression equivalent to 3^(-17)/8^(-14) with positive exponents only is (8^14)/(3^17).
Apply the Properties of Integer Exponents to generate equivalent expressions to (7^−3)^7 ⋅ 7^20/6^−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction.(1 point)
(7^−3)^7 ⋅ 7^20/6^−2=
(7^−3)^7 ⋅ 7^20/6^−2=
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we need to simplify each term separately.
First, let's simplify (7^(-3))^7.
Using the property of negative exponents, we can rewrite this as (1/7^3)^7.
Simplifying further, we have (1/343)^7.
Now, let's simplify 7^20 and 6^(-2) separately.
7^20 remains unchanged.
Using the property of negative exponents, we can rewrite 6^(-2) as 1/6^2.
Simplifying further, we have 1/36.
Now, we can combine the simplified terms:
(1/343)^7 * 7^20/36
To simplify this further, we can use the property of exponents.
(1/343)^7 is equivalent to 1^7/343^7, which is equal to 1/343^7.
So now we have 1/343^7 * 7^20/36.
Using the property of exponents, 7^20 can be written as (7^2)^10, which is equal to 49^10.
Now we have 1/343^7 * 49^10/36.
To simplify this expression, we can use the property of exponents.
343^7 can be written as (7^3)^7, which is equal to 343^7 = 7^21.
So now we have 1/7^21 * 49^10/36.
Simplifying 49^10 is not necessary at this point, as the 36 in the denominator cannot be simplified any further.
Therefore, the expression (7^(-3))^7 * 7^20/6^(-2) can be simplified to (1/7^21) * (49^10/36).
To obtain the final answer, we can perform the multiplication:
1/7^21 * 49^10/36 = (49^10)/(36 * 7^21).
This is the simplified expression, which cannot be further simplified into a simpler fraction.
First, let's simplify (7^(-3))^7.
Using the property of negative exponents, we can rewrite this as (1/7^3)^7.
Simplifying further, we have (1/343)^7.
Now, let's simplify 7^20 and 6^(-2) separately.
7^20 remains unchanged.
Using the property of negative exponents, we can rewrite 6^(-2) as 1/6^2.
Simplifying further, we have 1/36.
Now, we can combine the simplified terms:
(1/343)^7 * 7^20/36
To simplify this further, we can use the property of exponents.
(1/343)^7 is equivalent to 1^7/343^7, which is equal to 1/343^7.
So now we have 1/343^7 * 7^20/36.
Using the property of exponents, 7^20 can be written as (7^2)^10, which is equal to 49^10.
Now we have 1/343^7 * 49^10/36.
To simplify this expression, we can use the property of exponents.
343^7 can be written as (7^3)^7, which is equal to 343^7 = 7^21.
So now we have 1/7^21 * 49^10/36.
Simplifying 49^10 is not necessary at this point, as the 36 in the denominator cannot be simplified any further.
Therefore, the expression (7^(-3))^7 * 7^20/6^(-2) can be simplified to (1/7^21) * (49^10/36).
To obtain the final answer, we can perform the multiplication:
1/7^21 * 49^10/36 = (49^10)/(36 * 7^21).
This is the simplified expression, which cannot be further simplified into a simpler fraction.
Simplify the expression (4x^3)^2 using the properties of integer exponents.(1 point)
Responses
4x6
4 x superscript 6 baseline
16x6
16 x superscript 6 baseline
8x6
8 x superscript 6 baseline
16x^5
Responses
4x6
4 x superscript 6 baseline
16x6
16 x superscript 6 baseline
8x6
8 x superscript 6 baseline
16x^5
To simplify the expression (4x^3)^2 using the properties of integer exponents, we need to apply the power rule and multiply the exponents of 4 and x.
The power rule states that when we have a power raised to another power, we multiply the exponents.
In this case, (4x^3)^2 can be simplified as (4^2)(x^3)^2 = 16x^6.
Therefore, the simplified expression is 16x^6.
The power rule states that when we have a power raised to another power, we multiply the exponents.
In this case, (4x^3)^2 can be simplified as (4^2)(x^3)^2 = 16x^6.
Therefore, the simplified expression is 16x^6.
Apply the properties of integer exponents to generate an equivalent algebraic expression to (4x^4y^−4)^3/(x^7y^3)^2 .(1 point)
Responses
64x2y18
Start Fraction 64 over x squared y superscript 18 baseline End Fraction
x2y1864
Start Fraction x squared y superscript 18 baseline over 64 End Fraction
64x20
Start Fraction 64 over x superscript 20 baseline End Fraction
4/x^2y^18
Responses
64x2y18
Start Fraction 64 over x squared y superscript 18 baseline End Fraction
x2y1864
Start Fraction x squared y superscript 18 baseline over 64 End Fraction
64x20
Start Fraction 64 over x superscript 20 baseline End Fraction
4/x^2y^18
To generate an equivalent algebraic expression to (4x^4y^-4)^3/(x^7y^3)^2 using the properties of integer exponents, we need to simplify each term separately.
First, let's simplify (4x^4y^-4)^3.
Using the power rule, we can raise each term inside the parentheses to the power of 3:
(4^3)(x^4*3)(y^-4*3) = 64x^12y^-12.
Now, let's simplify (x^7y^3)^2.
Using the power rule, we can square each term inside the parentheses:
(x^7*2)(y^3*2) = x^14y^6.
Now that we have simplified both terms, we can rewrite the expression:
(64x^12y^-12)/(x^14y^6).
To combine these terms, we can use the properties of exponents:
64/x^2 * x^12/x^14 * 1/y^12 * y^6
Simplifying further, we get:
64/x^2 * x^(12-14) * y^(6-12)
= 64/x^2 * x^-2 * y^-6
= 64/(x^2 * x^2) * 1/(y^6)
= 64/(x^4 * y^6)
Therefore, the equivalent algebraic expression to (4x^4y^-4)^3/(x^7y^3)^2 is 64/(x^4 * y^6).
First, let's simplify (4x^4y^-4)^3.
Using the power rule, we can raise each term inside the parentheses to the power of 3:
(4^3)(x^4*3)(y^-4*3) = 64x^12y^-12.
Now, let's simplify (x^7y^3)^2.
Using the power rule, we can square each term inside the parentheses:
(x^7*2)(y^3*2) = x^14y^6.
Now that we have simplified both terms, we can rewrite the expression:
(64x^12y^-12)/(x^14y^6).
To combine these terms, we can use the properties of exponents:
64/x^2 * x^12/x^14 * 1/y^12 * y^6
Simplifying further, we get:
64/x^2 * x^(12-14) * y^(6-12)
= 64/x^2 * x^-2 * y^-6
= 64/(x^2 * x^2) * 1/(y^6)
= 64/(x^4 * y^6)
Therefore, the equivalent algebraic expression to (4x^4y^-4)^3/(x^7y^3)^2 is 64/(x^4 * y^6).
Thats not a answer
I apologize for the incorrect response.
To generate an equivalent algebraic expression to (4x^4y^-4)^3/(x^7y^3)^2 using the properties of integer exponents, we need to simplify each term separately.
First, let's simplify (4x^4y^-4)^3.
Using the power rule, we can raise each term inside the parentheses to the power of 3:
64x^12y^-12.
Now, let's simplify (x^7y^3)^2.
Using the power rule, we can square each term inside the parentheses:
x^(7*2)y^(3*2) = x^14y^6.
Now that we have simplified both terms, we can rewrite the expression:
(64x^12y^-12)/(x^14y^6).
To divide these terms, we can use the properties of exponents:
64/x^(12-14) * y^(-12-6) = 64/x^(-2) * y^(-18).
Now, using the property of negative exponents, we can move the terms with negative exponents to the denominator:
64/(x^2 * y^18).
Therefore, the equivalent algebraic expression to (4x^4y^-4)^3/(x^7y^3)^2 is 64/(x^2 * y^18).
To generate an equivalent algebraic expression to (4x^4y^-4)^3/(x^7y^3)^2 using the properties of integer exponents, we need to simplify each term separately.
First, let's simplify (4x^4y^-4)^3.
Using the power rule, we can raise each term inside the parentheses to the power of 3:
64x^12y^-12.
Now, let's simplify (x^7y^3)^2.
Using the power rule, we can square each term inside the parentheses:
x^(7*2)y^(3*2) = x^14y^6.
Now that we have simplified both terms, we can rewrite the expression:
(64x^12y^-12)/(x^14y^6).
To divide these terms, we can use the properties of exponents:
64/x^(12-14) * y^(-12-6) = 64/x^(-2) * y^(-18).
Now, using the property of negative exponents, we can move the terms with negative exponents to the denominator:
64/(x^2 * y^18).
Therefore, the equivalent algebraic expression to (4x^4y^-4)^3/(x^7y^3)^2 is 64/(x^2 * y^18).
Question
Apply the product rule of integer exponents to find the numerical equivalent of 12^−5⋅12^7 . Show your work and explain how you used the product rule of integer exponents.(2 points)
Apply the product rule of integer exponents to find the numerical equivalent of 12^−5⋅12^7 . Show your work and explain how you used the product rule of integer exponents.(2 points)
The product rule of integer exponents states that when multiplying two numbers with the same base but different exponents, you can add the exponents.
To find the numerical equivalent of 12^(-5) * 12^7, we can apply the product rule of integer exponents.
Let's rewrite the expression using the product rule:
12^(-5) * 12^7 = 12^(-5+7)
Simplifying the exponent, we have:
12^(2) = 144
Therefore, the numerical equivalent of 12^(-5) * 12^7 is 144.
We used the product rule of integer exponents by adding the exponents of 12 in the multiplication, which resulted in exponent 2. This allowed us to simplify the expression and obtain the numerical value.
To find the numerical equivalent of 12^(-5) * 12^7, we can apply the product rule of integer exponents.
Let's rewrite the expression using the product rule:
12^(-5) * 12^7 = 12^(-5+7)
Simplifying the exponent, we have:
12^(2) = 144
Therefore, the numerical equivalent of 12^(-5) * 12^7 is 144.
We used the product rule of integer exponents by adding the exponents of 12 in the multiplication, which resulted in exponent 2. This allowed us to simplify the expression and obtain the numerical value.
can u shorten that and make it sound like a teacher made it?
Certainly! Here's a shorter explanation in the style of a teacher:
To find the numerical value of 12^(-5) * 12^7, we can apply the product rule of integer exponents, which states that when multiplying two numbers with the same base, we add the exponents. In this case, we have 12 as the base and -5 and 7 as the exponents. Adding the exponents gives us -5 + 7 = 2. Therefore, the expression simplifies to 12^(2), which is equal to 144.
To find the numerical value of 12^(-5) * 12^7, we can apply the product rule of integer exponents, which states that when multiplying two numbers with the same base, we add the exponents. In this case, we have 12 as the base and -5 and 7 as the exponents. Adding the exponents gives us -5 + 7 = 2. Therefore, the expression simplifies to 12^(2), which is equal to 144.
can u keep it short but make it sound like a 5th grader made it
Sure! Here's a simplified explanation in the style of a 5th grader:
To find the answer when we multiply 12^(-5) and 12^7, we can add the exponents because the base (which is 12) is the same. When we add -5 and 7, we get 2. So, the answer is 12^2, which is 144.
To find the answer when we multiply 12^(-5) and 12^7, we can add the exponents because the base (which is 12) is the same. When we add -5 and 7, we get 2. So, the answer is 12^2, which is 144.
7 answers