Basic Math Examples

$2^{n - 1} \cdot 4^{n + 1} \cdot 16^{n}$

Step 1

Multiply $2^{n - 1} \cdot 4^{n + 1}$ .

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Step 1.1

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

$2^{n - 1} \cdot {(2^{2})}^{n + 1} \cdot 16^{n}$

Step 1.2

Multiply the exponents in ${(2^{2})}^{n + 1}$ .

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Step 1.2.1

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

$2^{n - 1} \cdot 2^{2 (n + 1)} \cdot 16^{n}$

Step 1.2.2

Apply the distributive property.

$2^{n - 1} \cdot 2^{2 n + 2 \cdot 1} \cdot 16^{n}$

Step 1.2.3

Multiply $2$ by $1$ .

$2^{n - 1} \cdot 2^{2 n + 2} \cdot 16^{n}$

Step 1.3

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

$2^{n - 1 + 2 n + 2} \cdot 16^{n}$

Step 1.4

Add $n$ and $2 n$ .

$2^{3 n - 1 + 2} \cdot 16^{n}$

Step 1.5

Add $- 1$ and $2$ .

$2^{3 n + 1} \cdot 16^{n}$

Step 2

Multiply $2^{3 n + 1} \cdot 16^{n}$ .

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Step 2.1

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

$2^{3 n + 1} \cdot {(2^{4})}^{n}$

Step 2.2

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

$2^{3 n + 1} \cdot 2^{4 n}$

Step 2.3

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

$2^{3 n + 1 + 4 n}$

Step 2.4

Add $3 n$ and $4 n$ .

$2^{7 n + 1}$