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

kuCAu

kuCAu

Answered question

2021-02-12

Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
8x23x

Answer & Explanation

Tasneem Almond

Tasneem Almond

Skilled2021-02-13Added 91 answers

Given:
8x23x
“For any rational exponent min in lowest terms, where m and n are integers and n > 0, we define
am/n=(an)m=amn
If nis even, then we require that a  0
Calculation:
Consider the given expression,
8x23x
Apply radical rule : abn=an bn in the numerator, we get
8x23=83  x23
=233  x23
=2x23
Substitute 8x23x=2x23 we get
By using the law of exponents,
2x23x=2x23x12
Apply exponent rule: xaxb=xa  b we get
2x23x13=2x23  12
=2x16
Final statement:
The simplyfied form of 8x23xis2x16

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