Question

Rewrite the rational exponent as a radical by extending the properties of integer exponents.

2 to the 7 over 8 power, all over 2 to the 1 over 4 power

A. √(2^7/8) / √(2^1/4)
B. ∛(2^7/8) / ∛(2^1/4)
C. ∛(2^7/8) / √(2^1/4)
D. √(2^7/8) / ∛(2^1/4)

Answer 1

To rewrite the rational exponent as a radical, we use the properties of integer exponents. Taking the given expression, 2^(7/8) / 2^(1/4), we can rewrite it as the 8th root of 2⁷divided by the 4th root of 2¹. Therefore, the answer is C.

Step-by-step explanation:

To rewrite the rational exponent as a radical, we can use the properties of integer exponents. We know that for any positive number x, xn/m can be written as the mth root of xn.

In this case, we have 27/8 divided by 21/4.

We can rewrite this as the 8th root of 27 divided by the 4th root of 21.

Therefore, the correct answer is option C: ∛(27/8) / √(21/4).