Solve 4^4/sqrt[4]{4}=128sqrt{2}

$$\frac{ { 4 }^{ 4 } }{ \sqrt[ 4 ]{ 4 } } = 128 \sqrt{ 2 }$$

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Solution Steps

Calculate 4 to the power of 4 and get 256.

$$\frac{256}{\sqrt[4]{4}}=128\sqrt{2}$$

Rewrite \sqrt[4]{4} as \sqrt[4]{2^{2}}. Convert from radical to exponential form and cancel out 2 in the exponent. Convert back to radical form.

$$\sqrt[4]{4}=\sqrt[4]{2^{2}}=2^{\frac{2}{4}}=2^{\frac{1}{2}}=\sqrt{2}$$

Insert the obtained value back in the expression.

$$\frac{256}{\sqrt{2}}=128\sqrt{2}$$

Rationalize the denominator of \frac{256}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{256\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=128\sqrt{2}$$

The square of \sqrt{2} is 2.

$$\frac{256\sqrt{2}}{2}=128\sqrt{2}$$

Divide 256\sqrt{2} by 2 to get 128\sqrt{2}.

$$128\sqrt{2}=128\sqrt{2}$$

Subtract 128\sqrt{2} from both sides.

$$128\sqrt{2}-128\sqrt{2}=0$$

Combine 128\sqrt{2} and -128\sqrt{2} to get 0.

$$0=0$$

Compare 0 and 0.

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