Question

Which expressions ar equivalent to the rational exponents.. Check all that apply.

Answer 1

Answers:

5^(3/2)

√(5^3)

Step-by-step explanation:

We will use the following properties:

`\begin{gathered} 5^a\cdot5^b=5^(a+b) \\ (5^a)^b=5^(a\cdot b) \end{gathered}`

So, the expression is equivalent to:

`(5^{(1)/(8)}\cdot5^{(3)/(8)})^3=(5^{(1)/(8)+(3)/(8)})^3`

Then, 1/8 + 3/8 is equal to:

`(1)/(8)+(3)/(8)=(1+3)/(8)=(4)/(8)=(1)/(2)`

So, the expression is:

`(5^{(1)/(8)+(3)/(8)})^3=(5^{(1)/(2)})^3=5^{(3)/(2)}`

Additionally, 5^(3/2) is also equal to:

`5^{(3)/(2)}=\sqrt[]{5^3}`

Therefore, the answers are the first and the third option.