Step-by-step Solution

Solve the product power $\sqrt[3]{x\sqrt[3]{x^{2\sqrt[3]{x\sqrt[3]{x^2}}}}}$

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Step-by-step explanation

Problem to solve:

$\left(x\left(x^{2\left(x\left(x^2\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}}\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}$

Learn how to solve power of a product problems step by step online.

$\sqrt[3]{xx^{\frac{2}{3}\sqrt[3]{x\sqrt[3]{x^{2}}}}}$

Unlock this full step-by-step solution!

Learn how to solve power of a product problems step by step online. Solve the product power (xx^(2(xx^2^0.3333333333333333)^0.3333333333333333)^0.3333333333333333)^0.3333333333333333. Applying the power of a power property. When multiplying exponents with same base you can add the exponents: x\sqrt[3]{x^{2}}. The power of a product is equal to the product of it's factors raised to the same power. Apply the exponent property of product of powers: x^a\cdot x^b=x^{a+b}.

Final Answer

$x^{\left(\frac{1}{3}+\frac{2}{9}\sqrt[9]{x^{5}}\right)}$
$\left(x\left(x^{2\left(x\left(x^2\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}}\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}$

Main topic:

Power of a product

Time to solve it:

~ 0.05 s (SnapXam)