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Simplify $\sqrt[3]{8^x}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $x$ and $n$ equals $\frac{1}{3}$
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$8^{\frac{1}{3}x}=65536$
Learn how to solve problems step by step online. Solve the equation with radicals 8^x^1/3=65536. Simplify \sqrt[3]{8^x} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals x and n equals \frac{1}{3}. We can take out the unknown from the exponent by applying logarithms in base 10 to both sides of the equation. Use the following rule for logarithms: \log_b(b^k)=k. Eliminate the \frac{1}{3} from the left side, multiplying both sides of the equation by the inverse of \frac{1}{3}.