Question

Write each expression with a single rational exponent. Show each step of your process. Which expressions are equivalent? Justify your reasoning.A. 4√x³B.1/x-1C. 10/x5x¹.x²D. x³x³x³

Answer 1

.

$\sqrt[4]{x^3}$

Using the law of indices:

$x^{\frac{1}{n}}=\sqrt[n]{x}$

So,

$\sqrt[4]{x^3\text{ }}=(x^3)^{\frac{1}{4}}$

Multiplying the powers

$x^{3\times\frac{1}{4}}\text{ }$

the final expression will be:

$x^{\frac{3}{4}}$

The final expression is x^(2/4)