Basic Math Examples

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

Step 1

Cancel the common factor of $2^{n}$ and $2^{2 n}$ .

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Step 1.1

Factor $2^{2 n}$ out of $2^{n} \cdot 8^{n}$ .

$\frac{2^{2 n} (2^{- n} \cdot 8^{n})}{2^{2 n} \cdot 16}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2^{2 n}$ out of $2^{2 n} \cdot 16$ .

$\frac{2^{2 n} (2^{- n} \cdot 8^{n})}{2^{2 n} (16)}$

Step 1.2.2

Cancel the common factor.

$\frac{2^{2 n} (2^{- n} \cdot 8^{n})}{2^{2 n} \cdot 16}$

Step 1.2.3

Rewrite the expression.

$\frac{2^{- n} \cdot 8^{n}}{16}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{2^{- n} \cdot {(2^{3})}^{n}}{16}$

Step 2.2

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

$\frac{2^{- n} \cdot 2^{3 n}}{16}$

Step 2.3

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

$\frac{2^{- n + 3 n}}{16}$

Step 2.4

Add $- n$ and $3 n$ .

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