Basic Math Examples

${({(\frac{4 n}{e})}^{4 n})}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $\frac{4 n}{e}$ .

${(\frac{{(4 n)}^{4 n}}{e^{4 n}})}^{2}$

Step 1.2

Apply the product rule to $4 n$ .

${(\frac{4^{4 n} n^{4 n}}{e^{4 n}})}^{2}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $\frac{4^{4 n} n^{4 n}}{e^{4 n}}$ .

$\frac{{(4^{4 n} n^{4 n})}^{2}}{{(e^{4 n})}^{2}}$

Step 2.2

Apply the product rule to $4^{4 n} n^{4 n}$ .

$\frac{{(4^{4 n})}^{2} {(n^{4 n})}^{2}}{{(e^{4 n})}^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

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

$\frac{4^{4 n \cdot 2} {(n^{4 n})}^{2}}{{(e^{4 n})}^{2}}$

Step 3.1.2

Multiply $2$ by $4$ .

$\frac{4^{8 n} {(n^{4 n})}^{2}}{{(e^{4 n})}^{2}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{4^{8 n} n^{4 n \cdot 2}}{{(e^{4 n})}^{2}}$

Step 3.2.2

Multiply $2$ by $4$ .

$\frac{4^{8 n} n^{8 n}}{{(e^{4 n})}^{2}}$

Step 4

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

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Step 4.1

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

$\frac{4^{8 n} n^{8 n}}{e^{4 n \cdot 2}}$

Step 4.2

Multiply $2$ by $4$ .

$\frac{4^{8 n} n^{8 n}}{e^{8 n}}$