Question

Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents. two to the seven eighths power, all over two to the one fourth power the eighth root of two to the fifth power the fifth root of two to the eighth power the square root of two to the five eighths power the fourth root of two to the sixth power

Answer 1

Answer:

The answer is " $\sqrt[8]{2^5}$ ".

Step-by-step explanation:

Given value:

$\to \frac{2 \frac{7}{8}}{2 \frac{1}{4}}$

They understand that, by using algebraic expressions laws, they subtract that inverse whenever we subtract powers with the same base. Every exponent's core is 2, therefore we subtract:

$\to \frac{7}{8} - \frac{1}{4}$

They have a shared denominator. It's least that is equally divided

among 8 or 2 is 8:

$\to \frac{7}{8} - \frac{2}{8}$

$\to \frac{7-2}{8}\\\\\to \frac{5}{8}$

This gives us:

$\to 2 \frac{5}{8}$

As rational notation is written as extremists, that root was its denominator as well as the power seems to be the numerator.

Which means 8 is the root and 5 the force that gives us:

$\sqrt[8]{2^5}$