which expression is correctly developed to use the product rule of exponents
A) 32^7
B) 10^8 x 10^8
C) (5^2)^9
D) 6^2 x 7^3
The correct expression that uses the product rule of exponents is:
B) 10^8 x 10^8
To find the numerical equivalent of 2^5 x 2^-2, we can use the product rule of exponents to add the exponents when we multiply like bases. Therefore, 2^5 x 2^-2 is equal to 2^(5+(-2)) = 2^3.
So, the correct answer is:
C) 8
Which of the following correctly used the product rule of exponents to simplify the expression 100^8 x 100^7
A) 100^56
B) 10,00^15
C) 100^15
D) 200^15
find the numerical equivalent 10^2 x 10^3
A) 1,100
B) 100,0000
C) 10^5
D) 10
find the numerical equivalent 2^5 x 2^-2
A) 2
B) 16
C) 8
D) 128
find the numerical equivalent 4^9 x 4^-7
A) 4^2
B) 4
C) 16
D) 4^16
To correctly apply the product rule of exponents, we need to multiply two or more exponents with the same base.
Let's go through each option and determine which one can be simplified using the product rule:
A) 32^7: This expression does not involve multiple exponents with the same base.
B) 10^8 x 10^8: This expression involves two exponents with the same base (10). To apply the product rule, we can add the exponents together: 10^8 x 10^8 = 10^(8+8) = 10^16.
C) (5^2)^9: In this expression, we have an exponent raised to another exponent. To simplify, we need to multiply the exponents: (5^2)^9 = 5^(2*9) = 5^18.
D) 6^2 x 7^3: Just like option B, this expression has two exponents with the same base (6 and 7). We can apply the product rule by multiplying the exponents together: 6^2 x 7^3 = 6^(2+3) x 7^3 = 6^5 x 7^3.
Based on the explanation above, the expression that is correctly developed to use the product rule of exponents is:
D) 6^2 x 7^3.
The correct answer is:
B) 10,000^15
To find the numerical equivalent of 10^2 x 10^3, we can use the product rule of exponents to add the exponents when we multiply like bases. Therefore, 10^2 x 10^3 is equal to 10^(2+3) = 10^5.
So, the correct answer is:
C) 10^5
To find the numerical equivalent of 4^9 x 4^-7, we can use the product rule of exponents to add the exponents when we multiply like bases. Therefore, 4^9 x 4^-7 is equal to 4^(9+(-7)) = 4^2.
So, the correct answer is:
A) 4^2