Question

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

Answer 1

Answer:

yes, the the fourth root of two is correct

Step-by-step explanation:

i just took the test today and got it correct

Answer 2

Answer:

$\sqrt[4]{2}$

Step-by-step explanation:

We start with the original problem:

$\frac{2^{3/4}}{2^{1/2}}$

So first we start by applying the quotient rule for powers, which tells you that whenever you are dividing two powers that have the same base and different power, you can copy the base and subtract the powers:

$\frac{b^{a}}{b^{c}}=b^{a-c}$

so:

$\frac{2^{3/4}}{2^{1/2}}=2^{\frac{3}{4}-\frac{1}{2}}$

which yields:

$2^{\frac{1}{4}}$

since we are talking about a rational exponent, we can next turn it into a radical by using the following rule:

$b^{\frac{1}{a}}=\sqrt[a]{b}$

so:

$2^{\frac{1}{4}}=\sqrt[4]{2}$