Question

Please help! Rewrite the rational exponent as a radical. (2 points)

Answer 1

Answer:

Answer: 3) $\sqrt{5}$

Step-by-step explanation:

Radical Form and Exponent Form

A radical can be expressed as a rational exponent following the identity:

$\displaystyle \sqrt[m]{x^n}=x^\frac{n}{m}$

We should also recall that:

$(x^n)^m=x^{nm}$

We are given the expression:

$\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}$

Applying the power of power:

$\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=\left(5^{\frac{3}{4}\cdot \frac{2}{3}}\right)$

Simplifying:

$\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=5^{\frac{1}{2}}$

Converting to radical form:

$\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=\sqrt{5}$

Answer: 3) $\sqrt{5}$