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

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

Answer 1

The correct answer is:

the eighth root of 2 to the fifth power .

Step-by-step explanation:

What we have is:

`\frac{2^{(7)/(8)}}{2^{(1)/(4)}}`

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:

`2^{(5)/(8)}`

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:

`\sqrt[8]{2^5}`,

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