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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 differential calculus 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}. Decompose 8 in it's prime factors. Simplify \left(2^{3}\right)^{\frac{1}{3}x} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals \frac{1}{3}x. We can take out the unknown from the exponent by applying logarithms in base 10 to both sides of the equation.