Pre-Algebra Examples

${(\frac{- 4 y^{4}}{3})}^{4}$

Step 1

Move the negative in front of the fraction.

${(- \frac{4 y^{4}}{3})}^{4}$

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 $- \frac{4 y^{4}}{3}$ .

${(- 1)}^{4} {(\frac{4 y^{4}}{3})}^{4}$

Step 2.2

Apply the product rule to $\frac{4 y^{4}}{3}$ .

${(- 1)}^{4} \frac{{(4 y^{4})}^{4}}{3^{4}}$

Step 2.3

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

${(- 1)}^{4} \frac{4^{4} {(y^{4})}^{4}}{3^{4}}$

Step 3

Simplify the expression.

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Step 3.1

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

$1 \frac{4^{4} {(y^{4})}^{4}}{3^{4}}$

Step 3.2

Multiply $\frac{4^{4} {(y^{4})}^{4}}{3^{4}}$ by $1$ .

$\frac{4^{4} {(y^{4})}^{4}}{3^{4}}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{256 {(y^{4})}^{4}}{3^{4}}$

Step 4.2

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

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Step 4.2.1

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

$\frac{256 y^{4 \cdot 4}}{3^{4}}$

Step 4.2.2

Multiply $4$ by $4$ .

$\frac{256 y^{16}}{3^{4}}$

Step 5

Raise $3$ to the power of $4$ .

$\frac{256 y^{16}}{81}$