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

the eighth root of 2 to the fifth power

the fifth root of 2 to the eighth power

the square root of 2 to the 5 over 8 power

the fourth root of 2 to the sixth power

A. 2^(7/8) / 2^(1/4) = 2^(7/8) / 2^(2/8) = 2^(5/8)B. ( 2^(1/8) ) 5 = 2^(5/8)C. 2^(8/5)D. 2^(5/8)E. ( 2^(5/8) )^(1/2) = 2^(5/16)F. ( 2^6 )^(1/4) = 2^(6/4) = 2^(1/3)

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MsEHolt MsEHolt · Answer 2 · 2018-07-13T04:14:23+02:00

The correct answer is:

the eighth root of 2 to the fifth power .

Explanation:

What we have is:

[tex] \frac{2^{\frac{7}{8}}}{2^{\frac{1}{4}}} [/tex]

Using the rules of exponents, we know that when we divide powers with the same base, we subtract the exponents. The base of each exponent is 2, so we subtract:

7/8 - 1/4

We find a common denominator. The smallest thing that both 8 and 2 will evenly divide into is 8:

7/8 - 2/8 = 5/8

This gives us:

[tex] 2^{\frac{5}{8}} [/tex]

When rewriting rational exponents as radicals, the denominator is the root and the numerator is the power. This means that 8 is the root and 5 is the power, which gives us:

[tex] \sqrt[8]{2^5} [/tex],

or in words, the eighth root of 2 to the fifth power.