7(27×6)1/3

Question

7(27×6)1/3

ScanSolve AI Tutor · Accepted Answer

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

The problem is $(27x^6)^{\frac{1}{3}}$ . We need to apply the exponent $\frac{1}{3}$ to both the numerical coefficient and the variable term inside the parentheses.

Apply the exponent to each factor inside the parentheses.
$(27x^6)^{\frac{1}{3}} = 27^{\frac{1}{3}} \cdot (x^6)^{\frac{1}{3}}$
Evaluate $27^{\frac{1}{3}}$ .
This means finding the cube root of 27.
We know that $3 \times 3 \times 3 = 27$ .
So, $27^{\frac{1}{3}} = 3$ .
Evaluate $(x^6)^{\frac{1}{3}}$ using the power of a power rule $(a^m)^n = a^{m \times n}$ .
$(x^6)^{\frac{1}{3}} = x^{6 \times \frac{1}{3}} = x^{\frac{6}{3}} = x^2$
Combine the simplified terms.
$3 \cdot x^2 = 3x^2$
The simplified expression is $\boxed*{3x^2}$ .

7(27x6)1/3

Step-by-step solution

Apply the exponent to each factor inside the parentheses.

Evaluate $27^{\frac{1}{3}}$ .

Evaluate $(x^6)^{\frac{1}{3}}$ using the power of a power rule $(a^m)^n = a^{m \times n}$ .

Combine the simplified terms.

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