Pre-Algebra Examples

${(- \frac{2 q^{4}}{7})}^{4}$

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 $- \frac{2 q^{4}}{7}$ .

${(- 1)}^{4} {(\frac{2 q^{4}}{7})}^{4}$

Step 1.2

Apply the product rule to $\frac{2 q^{4}}{7}$ .

${(- 1)}^{4} \frac{{(2 q^{4})}^{4}}{7^{4}}$

Step 1.3

Apply the product rule to $2 q^{4}$ .

${(- 1)}^{4} \frac{2^{4} {(q^{4})}^{4}}{7^{4}}$

Step 2

Simplify the expression.

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Step 2.1

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

$1 \frac{2^{4} {(q^{4})}^{4}}{7^{4}}$

Step 2.2

Multiply $\frac{2^{4} {(q^{4})}^{4}}{7^{4}}$ by $1$ .

$\frac{2^{4} {(q^{4})}^{4}}{7^{4}}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{16 {(q^{4})}^{4}}{7^{4}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{16 q^{4 \cdot 4}}{7^{4}}$

Step 3.2.2

Multiply $4$ by $4$ .

$\frac{16 q^{16}}{7^{4}}$

Step 4

Raise $7$ to the power of $4$ .

$\frac{16 q^{16}}{2401}$