Simplify (100^(2/3))^(3/4)

${(100^{\frac{2}{3}})}^{\frac{3}{4}}$

Simplify the expression.

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Multiply the exponents in ${(100^{\frac{2}{3}})}^{\frac{3}{4}}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$100^{\frac{2}{3} \cdot \frac{3}{4}}$

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

$100^{\frac{2}{3} \cdot \frac{3}{2 (2)}}$

Cancel the common factor.

$100^{\frac{2}{3} \cdot \frac{3}{2 \cdot 2}}$

Rewrite the expression.

$100^{\frac{1}{3} \cdot \frac{3}{2}}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$100^{\frac{1}{3} \cdot \frac{3}{2}}$

Rewrite the expression.

$100^{\frac{1}{2}}$

Rewrite $100$ as $10^{2}$ .

${(10^{2})}^{\frac{1}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10^{2 (\frac{1}{2})}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$10^{2 (\frac{1}{2})}$

Rewrite the expression.

$10^{1}$

Evaluate the exponent.

$10$

Simplify (100^(2/3))^(3/4)

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