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(8x^(2))^((2)/(3))=

$\left(8 x^{2}\right)^{\frac{2}{3}}=$

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Powers with negative bases

Full solution

Q.

\left(8 x^{2}\right)^{\frac{2}{3}}=

Apply Power Rule: Evaluate the expression using the power of a power rule, which states that $(a^m)^n = a^{m*n}$ . $(8x^{2})^{\frac{2}{3}} = 8^{\frac{2}{3}} \times (x^{2})^{\frac{2}{3}}$
Simplify $8^{\frac{2}{3}}$ : Simplify $8^{\frac{2}{3}}$ . Since $8$ is $2^3$ , we can rewrite $8$ as $2^3$ and then apply the power of a power rule. $\newline$ $8^{\frac{2}{3}} = (2^3)^{\frac{2}{3}} = 2^{3*\frac{2}{3}} = 2^2 = 4$
Simplify $(x^{2})^{\frac{2}{3}}$ : Simplify $(x^{2})^{\frac{2}{3}}$ . Using the power of a power rule again, we multiply the exponents. $(x^{2})^{\frac{2}{3}} = x^{2*\frac{2}{3}} = x^{\frac{4}{3}}$
Combine Terms: Combine the simplified terms to get the final answer. $4 \times x^{\frac{4}{3}}$

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