Basic Math Examples

$\frac{16^{\frac{3}{4}}}{8^{\frac{1}{3}}} \div \frac{2^{4}}{8^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{16^{\frac{3}{4}}}{8^{\frac{1}{3}}} \cdot \frac{8^{2}}{2^{4}}$

Step 2

Combine.

$\frac{16^{\frac{3}{4}} \cdot 8^{2}}{8^{\frac{1}{3}} \cdot 2^{4}}$

Step 3

Move $8^{\frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{16^{\frac{3}{4}} \cdot 8^{2} \cdot 8^{- \frac{1}{3}}}{2^{4}}$

Step 4

Multiply $8^{2}$ by $8^{- \frac{1}{3}}$ by adding the exponents.

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Step 4.1

Move $8^{- \frac{1}{3}}$ .

$\frac{16^{\frac{3}{4}} \cdot (8^{- \frac{1}{3}} \cdot 8^{2})}{2^{4}}$

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{16^{\frac{3}{4}} \cdot 8^{- \frac{1}{3} + 2}}{2^{4}}$

Step 4.3

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{16^{\frac{3}{4}} \cdot 8^{- \frac{1}{3} + 2 \cdot \frac{3}{3}}}{2^{4}}$

Step 4.4

Combine $2$ and $\frac{3}{3}$ .

$\frac{16^{\frac{3}{4}} \cdot 8^{- \frac{1}{3} + \frac{2 \cdot 3}{3}}}{2^{4}}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{16^{\frac{3}{4}} \cdot 8^{\frac{- 1 + 2 \cdot 3}{3}}}{2^{4}}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $2$ by $3$ .

$\frac{16^{\frac{3}{4}} \cdot 8^{\frac{- 1 + 6}{3}}}{2^{4}}$

Step 4.6.2

Add $- 1$ and $6$ .

$\frac{16^{\frac{3}{4}} \cdot 8^{\frac{5}{3}}}{2^{4}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $16$ as $2^{4}$ .

$\frac{{(2^{4})}^{\frac{3}{4}} \cdot 8^{\frac{5}{3}}}{2^{4}}$

Step 5.2

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

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Step 5.2.1

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

$\frac{2^{4 (\frac{3}{4})} \cdot 8^{\frac{5}{3}}}{2^{4}}$

Step 5.2.2

Cancel the common factor of $4$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{2^{4 (\frac{3}{4})} \cdot 8^{\frac{5}{3}}}{2^{4}}$

Step 5.2.2.2

Rewrite the expression.

$\frac{2^{3} \cdot 8^{\frac{5}{3}}}{2^{4}}$

Step 5.3

Rewrite $8$ as $2^{3}$ .

$\frac{2^{3} \cdot {(2^{3})}^{\frac{5}{3}}}{2^{4}}$

Step 5.4

Multiply the exponents in ${(2^{3})}^{\frac{5}{3}}$ .

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Step 5.4.1

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

$\frac{2^{3} \cdot 2^{3 (\frac{5}{3})}}{2^{4}}$

Step 5.4.2

Cancel the common factor of $3$ .

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Step 5.4.2.1

Cancel the common factor.

$\frac{2^{3} \cdot 2^{3 (\frac{5}{3})}}{2^{4}}$

Step 5.4.2.2

Rewrite the expression.

$\frac{2^{3} \cdot 2^{5}}{2^{4}}$

Step 5.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2^{3 + 5}}{2^{4}}$

Step 5.6

Add $3$ and $5$ .

$\frac{2^{8}}{2^{4}}$

Step 6

Simplify the expression.

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Step 6.1

Raise $2$ to the power of $4$ .

$\frac{2^{8}}{16}$

Step 6.2

Raise $2$ to the power of $8$ .

$\frac{256}{16}$

Step 6.3

Divide $256$ by $16$ .

$16$