Which of the following correctly used the product rule of exponents to simplify the expression

Question

100⁸ x 100⁷
A. 100¹⁵
B. 200¹⁵
C. 100⁵⁶
D. 10,000¹⁵

Answer 1

The product rule of exponents states that when you multiply two numbers with the same base, you add their exponents.

In this case, both numbers have a base of 100. The exponents are 8 and 7. To simplify, you need to add the exponents:

100⁸ x 100⁷ = 100^(8+7) = 100¹⁵

Therefore, the correct answer is A. 100¹⁵.

Answer 2

Find the numerical equivalent of 10² x 10³
A. 1,100
B. 10⁵
C. 10
D. 100,000

Answer 3

To find the numerical equivalent of 10² x 10³, you need to multiply the numbers together:

10² x 10³ = 10^(2+3) = 10⁵

Therefore, the correct answer is B. 10⁵.

Answer 4

Find the numerical equivalent of 2⁵ x 2-²
A. 8
B. 128
C. 16
D. 2

Answer 5

To find the numerical equivalent of 2⁵ x 2⁻², you need to multiply the numbers together:

2⁵ x 2⁻² = 2^(5 - 2) = 2³ = 8

Therefore, the correct answer is A. 8.

Answer 6

Find the numerical equivalent of 4⁹ x 4-⁷
A. 16
B. 4²
C. 4¹⁶
D. 4

Answer 7

To find the numerical equivalent of 4⁹ x 4⁻⁷, you need to multiply the numbers together:

4⁹ x 4⁻⁷ = 4^(9 - 7) = 4² = 16

Therefore, the correct answer is A. 16.