Question
use the Product Rule of Exponents to simplify 5^10 * 5^5
A. 5^15
B. 5^50
C. 25^50
D.25^15
A. 5^15
B. 5^50
C. 25^50
D.25^15
Answers
Answer
What is the missing exponent in the following equation
h^450/h^?
h^450/h^?
Answer
What is the missing exponent in the following equation
h^450/h^? = h^215
h^450/h^? = h^215
Answer
Simplify 12^87 divided by 12^25
Answer
What is the value of 6.9 - 2^0
A. 5.9
B. 7.9
C. 6.9
D. 4.9
A. 5.9
B. 7.9
C. 6.9
D. 4.9
Answer
9 8 (-33)^0 + 3/2(8 - 27^0) = __ * __ + 3/2(__-__)
Answer
158^0/5 + 4 (7^0 - 6) = __
Answer
Use the Power Rule of Exponents to simplify (10^3)^6
Answer
use the Power rule of Exponents to create a simplified equivalent expression for (19^4)^9
Answer
Apply the Property of Negative Integer Exponents to solve 7^-3. the answer should not contain any exponent expression or decimals.
Answer
Apply the Properties of integer Exponents to generate equivalent expressions to (7^-3)^7 *7^20/6^-2
Answer
Simplify the expression (4x^3)^2 using the properties of integer exponents.
A. 8x^6
B. 16x^5
C. 4x^6
D. 16x^6
A. 8x^6
B. 16x^5
C. 4x^6
D. 16x^6
Answer
apply the product rule of integer exponents to find the numerical equivalent of 12^-5 * 12^7
Answered by
GPT 3.5
According to the Product Rule of Exponents, when multiplying two powers with the same base, you add the exponents.
In this case, 5^10 * 5^5 can be simplified as 5^(10+5) = 5^15.
Therefore, the answer is A. 5^15.
In this case, 5^10 * 5^5 can be simplified as 5^(10+5) = 5^15.
Therefore, the answer is A. 5^15.
Answered by
GPT 3.5
We can use the Quotient Rule of Exponents here, which states that when dividing two powers with the same base, you subtract the exponent of the denominator from the exponent of the numerator.
In this case, h^450/h^? can be simplified as h^(450-?).
To find the missing exponent, we need more information or context.
In this case, h^450/h^? can be simplified as h^(450-?).
To find the missing exponent, we need more information or context.
Answered by
GPT 3.5
We can use the Quotient Rule of Exponents here, which states that when dividing two powers with the same base, you subtract the exponent of the denominator from the exponent of the numerator.
In this case, h^450/h^? can be simplified as h^(450-?).
The equation is h^(450-?) = h^215.
To find the missing exponent, we can equate the exponents:
450 - ? = 215
To isolate the missing exponent, we can subtract 215 from both sides of the equation:
-? = 215 - 450
-? = -235
Finally, to solve for the missing exponent, we can multiply both sides of the equation by -1, remembering that multiplying or dividing both sides of an equation by a negative number reverses the direction of the inequality:
? = 235
Therefore, the missing exponent in the equation h^450/h^? = h^215 is 235.
In this case, h^450/h^? can be simplified as h^(450-?).
The equation is h^(450-?) = h^215.
To find the missing exponent, we can equate the exponents:
450 - ? = 215
To isolate the missing exponent, we can subtract 215 from both sides of the equation:
-? = 215 - 450
-? = -235
Finally, to solve for the missing exponent, we can multiply both sides of the equation by -1, remembering that multiplying or dividing both sides of an equation by a negative number reverses the direction of the inequality:
? = 235
Therefore, the missing exponent in the equation h^450/h^? = h^215 is 235.
Answered by
GPT 3.5
According to the Quotient Rule of Exponents, when dividing two powers with the same base, you subtract the exponent of the denominator from the exponent of the numerator.
In this case, 12^87 divided by 12^25 can be simplified as 12^(87-25).
Therefore, the expression simplifies to 12^62.
In this case, 12^87 divided by 12^25 can be simplified as 12^(87-25).
Therefore, the expression simplifies to 12^62.
Answered by
GPT 3.5
2^0 equals 1, so we can substitute that into the equation:
6.9 - 1
This simplifies to:
5.9
Therefore, the value of 6.9 - 2^0 is A. 5.9.
6.9 - 1
This simplifies to:
5.9
Therefore, the value of 6.9 - 2^0 is A. 5.9.
Answered by
GPT 3.5
To simplify the expression 9 8 (-33)^0 + 3/2(8 - 27^0), we need to apply the operation of exponentiation first.
(-33)^0 is equal to 1, so we can substitute that into the equation:
9 8 (1) + 3/2(8 - 1)
This simplifies to:
9 8 + 3/2(8 - 1)
Next, we simplify the terms inside the parentheses:
9 8 + 3/2(7)
To evaluate the multiplication of 3/2 and 7, we multiply the numerators and denominators:
9 8 + (21/2)
Since 9 8 can be written as 96, we have:
96 + (21/2)
To add these fractions, we need a common denominator:
96 + (21/2) = (192/2) + (21/2) = (192 + 21)/2 = 213/2
Therefore, the simplified expression is:
96 + (21/2) = 213/2
So, the missing numbers in the equation __ * __ + 3/2(__-__) are 213/2.
(-33)^0 is equal to 1, so we can substitute that into the equation:
9 8 (1) + 3/2(8 - 1)
This simplifies to:
9 8 + 3/2(8 - 1)
Next, we simplify the terms inside the parentheses:
9 8 + 3/2(7)
To evaluate the multiplication of 3/2 and 7, we multiply the numerators and denominators:
9 8 + (21/2)
Since 9 8 can be written as 96, we have:
96 + (21/2)
To add these fractions, we need a common denominator:
96 + (21/2) = (192/2) + (21/2) = (192 + 21)/2 = 213/2
Therefore, the simplified expression is:
96 + (21/2) = 213/2
So, the missing numbers in the equation __ * __ + 3/2(__-__) are 213/2.
Answered by
GPT 3.5
To simplify the expression 158^0/5 + 4 (7^0 - 6), we need to evaluate the exponentiation first.
Any number (except 0) raised to the power of 0 is equal to 1. Therefore, we can simplify 158^0 to 1:
1/5 + 4 (1 - 6)
Next, we simplify the terms inside the parentheses:
1/5 + 4 (-5)
Multiplying 4 by -5 gives us:
1/5 - 20
To add these fractions, we need a common denominator:
1/5 - 20 = 1/5 - (20/1) = 1/5 - (100/5) = (1 - 100)/5 = -99/5
Therefore, the simplified expression is:
-99/5
So, the missing number in the equation __ = -99/5.
Any number (except 0) raised to the power of 0 is equal to 1. Therefore, we can simplify 158^0 to 1:
1/5 + 4 (1 - 6)
Next, we simplify the terms inside the parentheses:
1/5 + 4 (-5)
Multiplying 4 by -5 gives us:
1/5 - 20
To add these fractions, we need a common denominator:
1/5 - 20 = 1/5 - (20/1) = 1/5 - (100/5) = (1 - 100)/5 = -99/5
Therefore, the simplified expression is:
-99/5
So, the missing number in the equation __ = -99/5.
Answered by
GPT 3.5
The Power Rule of Exponents states that when raising a power to another exponent, you multiply the exponents.
Using this rule, we can simplify (10^3)^6 as 10^(3*6).
Multiplying the exponents, we get 10^18.
Therefore, (10^3)^6 simplifies to 10^18.
Using this rule, we can simplify (10^3)^6 as 10^(3*6).
Multiplying the exponents, we get 10^18.
Therefore, (10^3)^6 simplifies to 10^18.
Answered by
GPT 3.5
According to the Power Rule of Exponents, when raising a power to another exponent, you multiply the exponents:
(19^4)^9 can be rewritten as 19^(4*9).
Therefore, (19^4)^9 is equivalent to 19^36.
(19^4)^9 can be rewritten as 19^(4*9).
Therefore, (19^4)^9 is equivalent to 19^36.
Answered by
GPT 3.5
The Property of Negative Integer Exponents states that for any non-zero number, the negative exponent can be rewritten as 1 divided by the number raised to the positive exponent:
7^(-3) = 1 / 7^3.
Therefore, 7^-3 is equivalent to 1 divided by 7^3, which can also be written as 1/343.
7^(-3) = 1 / 7^3.
Therefore, 7^-3 is equivalent to 1 divided by 7^3, which can also be written as 1/343.
Answered by
GPT 3.5
Using the Properties of Integer Exponents, we can simplify the expression (7^-3)^7 * 7^20 / 6^-2 as follows:
(7^-3)^7 * 7^20 / 6^-2
Since (7^-3)^7 means raising 7^-3 to the 7th power, we can apply the Property of power of a power to get:
7^(-3*7) * 7^20 / 6^-2
Simplifying further, we have:
7^-21 * 7^20 / 6^-2
Applying the Property of multiplying powers with the same base, we add the exponents:
7^(-21 + 20) / 6^-2
Now, simplifying the exponents:
7^-1 / 6^-2
Using the Property of negative exponents, we can rewrite 7^-1 and 6^-2 as the reciprocals of their positive exponents:
1/7^1 / 1/6^2
Simplifying further, we have:
6^2 / 7^1
Finally, evaluating the numerical values:
6^2 = 36
7^1 = 7
Hence, the expression (7^-3)^7 * 7^20 / 6^-2 is equivalent to 36/7.
(7^-3)^7 * 7^20 / 6^-2
Since (7^-3)^7 means raising 7^-3 to the 7th power, we can apply the Property of power of a power to get:
7^(-3*7) * 7^20 / 6^-2
Simplifying further, we have:
7^-21 * 7^20 / 6^-2
Applying the Property of multiplying powers with the same base, we add the exponents:
7^(-21 + 20) / 6^-2
Now, simplifying the exponents:
7^-1 / 6^-2
Using the Property of negative exponents, we can rewrite 7^-1 and 6^-2 as the reciprocals of their positive exponents:
1/7^1 / 1/6^2
Simplifying further, we have:
6^2 / 7^1
Finally, evaluating the numerical values:
6^2 = 36
7^1 = 7
Hence, the expression (7^-3)^7 * 7^20 / 6^-2 is equivalent to 36/7.
Answered by
GPT 3.5
To simplify the expression (4x^3)^2 using the Properties of Integer Exponents, we can apply the Property of Power of a Power:
(4x^3)^2 = 4^2 * (x^3)^2.
Simplifying further:
4^2 = 16
(x^3)^2 = x^(3*2) = x^6.
Therefore, (4x^3)^2 simplifies to 16x^6.
The correct answer is D. 16x^6.
(4x^3)^2 = 4^2 * (x^3)^2.
Simplifying further:
4^2 = 16
(x^3)^2 = x^(3*2) = x^6.
Therefore, (4x^3)^2 simplifies to 16x^6.
The correct answer is D. 16x^6.
Answered by
GPT 3.5
The Product Rule of Integer Exponents states that when multiplying two powers with the same base, you add the exponents.
For the expression 12^-5 * 12^7, we can apply the Product Rule of Integer Exponents to combine the two powers:
12^-5 * 12^7 = 12^(-5 + 7).
Simplifying the exponent:
12^2 = 12^(7 - 5) = 12^2.
Therefore, 12^-5 * 12^7 is equal to 12^2.
The numerical equivalent of 12^2 is 144.
Hence, 12^-5 * 12^7 is equal to 144.
For the expression 12^-5 * 12^7, we can apply the Product Rule of Integer Exponents to combine the two powers:
12^-5 * 12^7 = 12^(-5 + 7).
Simplifying the exponent:
12^2 = 12^(7 - 5) = 12^2.
Therefore, 12^-5 * 12^7 is equal to 12^2.
The numerical equivalent of 12^2 is 144.
Hence, 12^-5 * 12^7 is equal to 144.
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