Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. frac{sqrt[3]{8x^{2}}}{sqrt{x}}

Kye

Kye

Answered question

2021-03-05

Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
3{8x2}x

Answer & Explanation

Mayme

Mayme

Skilled2021-03-06Added 103 answers

Step 1
3{8x2}x
Law of exponents:
amn=(n{a})m=n{am}
If n is even, then we require that a0
Step 2
Consider the given expression,
1) 3{8x2}x
Apply radical rule: n{ab}=n{a}n{b} in the numerator, we get
3{8x2}=3{8}3{x2}
=3{23}3{x2}
=23{x2}
Substitute 3{8x2}=23{x2} in equation (1), we get
23{x2}x=2x23x12
Apply exponent rule: xaxb=xab, we get
2x23x12=2x2312
=2x16
The simplified form of 3{8x2}x is 2x16
Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-27Added 2605 answers

Answer is given below (on video)

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