Simplify (32×10)^(1/6)

Question

ScanSolve AI Tutor · Accepted Answer

let's simplify this expression using the rules of indices.

The problem is $(32x^{10})^{\frac{1}{5}}$ . We need to apply the exponent $\frac{1}{5}$ to both the numerical coefficient and the variable term inside the parentheses.

Apply the exponent to each factor inside the parentheses.
$(32x^{10})^{\frac{1}{5}} = 32^{\frac{1}{5}} \cdot (x^{10})^{\frac{1}{5}}$
Evaluate $32^{\frac{1}{5}}$ .
This means finding the fifth root of 32.
We know that $2 \times 2 \times 2 \times 2 \times 2 = 32$ .
So, $32^{\frac{1}{5}} = 2$ .
Evaluate $(x^{10})^{\frac{1}{5}}$ using the power of a power rule $(a^m)^n = a^{m \times n}$ .
$(x^{10})^{\frac{1}{5}} = x^{10 \times \frac{1}{5}} = x^{\frac{10}{5}} = x^2$
Combine the simplified terms.
$2 \cdot x^2 = 2x^2$
The simplified expression is $\boxed*{2x^2}$ .

Simplify (32x10)^(1/6)

Step-by-step solution

Apply the exponent to each factor inside the parentheses.

Evaluate $32^{\frac{1}{5}}$ .

Evaluate $(x^{10})^{\frac{1}{5}}$ using the power of a power rule $(a^m)^n = a^{m \times n}$ .

Combine the simplified terms.

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