GMAT Exponents: Which of the following is equivalent…
Question
Which of the following is equivalent to (10^2)^(n+1)?
- 10^2(10^(2n))
- 10^2(10^(n+1))
- 10^(2n+3)
- 10(10^(2n))
- (10^(2n))^2
Topics: exponents
Solution
Step 1
We apply the exponent-of-a-power rule to simplify the nested exponent.
(10^2)^(n+1) = 10^(2(n+1))
Step 2
We distribute the exponent multiplication inside the parentheses.
2(n+1) = 2n + 2
Step 3
We use the property of multiplying exponents with the same base to split the result into a product.
10^(2n+2) = 10^2 × 10^(2n)
Answer
10^2(10^(2n)) (A)
