Basic Math Examples

${(\frac{- 2 b}{a^{4}})}^{4}$

Step 1

Move the negative in front of the fraction.

${(- \frac{2 b}{a^{4}})}^{4}$

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 $- \frac{2 b}{a^{4}}$ .

${(- 1)}^{4} {(\frac{2 b}{a^{4}})}^{4}$

Step 2.2

Apply the product rule to $\frac{2 b}{a^{4}}$ .

${(- 1)}^{4} \frac{{(2 b)}^{4}}{{(a^{4})}^{4}}$

Step 2.3

Apply the product rule to $2 b$ .

${(- 1)}^{4} \frac{2^{4} b^{4}}{{(a^{4})}^{4}}$

Step 3

Raise $- 1$ to the power of $4$ .

$1 \frac{2^{4} b^{4}}{{(a^{4})}^{4}}$

Step 4

Multiply $\frac{2^{4} b^{4}}{{(a^{4})}^{4}}$ by $1$ .

$\frac{2^{4} b^{4}}{{(a^{4})}^{4}}$

Step 5

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

$\frac{16 b^{4}}{{(a^{4})}^{4}}$

Step 6

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

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Step 6.1

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

$\frac{16 b^{4}}{a^{4 \cdot 4}}$

Step 6.2

Multiply $4$ by $4$ .

$\frac{16 b^{4}}{a^{16}}$