b) $$ \left(x^{\frac{2}{3}}\right)^{6} $$

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UpStudy AI · Accepted Answer

To simplify the expression $$ \left(x^{\frac{2}{3}}\right)^{6} $$, you can use the **laws of exponents**, specifically the power of a power rule. Here's a step-by-step breakdown:

### Power of a Power Rule
The power of a power rule states that:
$$
\left(x^{a}\right)^{b} = x^{a \times b}
$$

### Applying the Rule
Given the expression:
$$
\left(x^{\frac{2}{3}}\right)^{6}
$$
Apply the power of a power rule by multiplying the exponents:
$$
x^{\frac{2}{3} \times 6}
$$

### Simplifying the Exponent
Multiply $$\frac{2}{3}$$ by $$6$$:
$$
\frac{2}{3} \times 6 = 4
$$

### Final Simplified Form
So, the expression simplifies to:
$$
x^{4}
$$

### Summary
$$
\left(x^{\frac{2}{3}}\right)^{6} = x^{4}
$$

This simplification shows that raising $$x^{\frac{2}{3}}$$ to the 6th power results in $$x^4$$.
$$ \left(x^{\frac{2}{3}}\right)^{6} = x^{4} $$

b) \( \left(x^{\frac{2}{3}}\right)^{6} \)

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