Basic Math Examples

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

Step 1

Simplify the expression.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

Factor $2$ out of $4$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.1.3

Cancel the common factor of $3$ .

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Step 1.1.3.1

Cancel the common factor.

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

Step 1.1.3.2

Rewrite the expression.

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

$10^{1}$

Step 3

Evaluate the exponent.

$10$