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^{(1)/(n)}=\sqrt[n]{x}`

So,

`\sqrt[4]{x^3\text{ }}=(x^3)^{(1)/(4)}`

Multiplying the powers

`x^{3*(1)/(4)}\text{ }`

the final expression will be:

`x^{(3)/(4)}`

The final expression is x^(2/4)