Basic Math Examples

${(8^{\frac{4}{3}})}^{5} \cdot 4^{- 4} \div 16^{2}$

Step 1

Rewrite the division as a fraction.

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

Step 2

Move $4^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Multiply $4$ by $2$ .

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

Step 3.3

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

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

Step 3.4

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

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Step 3.4.1

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

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

Step 3.4.2

Multiply $2$ by $4$ .

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

Step 3.5

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

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

Step 3.6

Add $8$ and $8$ .

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

Step 4

Simplify the numerator.

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Step 4.1

Multiply the exponents in ${(8^{\frac{4}{3}})}^{5}$ .

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Step 4.1.1

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

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

Step 4.1.2

Multiply $\frac{4}{3} \cdot 5$ .

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Step 4.1.2.1

Combine $\frac{4}{3}$ and $5$ .

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

Step 4.1.2.2

Multiply $4$ by $5$ .

$\frac{8^{\frac{20}{3}}}{2^{16}}$

Step 4.2

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

$\frac{{(2^{3})}^{\frac{20}{3}}}{2^{16}}$

Step 4.3

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

$\frac{2^{3 (\frac{20}{3})}}{2^{16}}$

Step 4.4

Cancel the common factor of $3$ .

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Step 4.4.1

Cancel the common factor.

$\frac{2^{3 (\frac{20}{3})}}{2^{16}}$

Step 4.4.2

Rewrite the expression.

$\frac{2^{20}}{2^{16}}$

Step 4.5

Raise $2$ to the power of $20$ .

$\frac{1048576}{2^{16}}$

Step 5

Simplify the expression.

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Step 5.1

Raise $2$ to the power of $16$ .

$\frac{1048576}{65536}$

Step 5.2

Divide $1048576$ by $65536$ .

$16$