Algebra Examples

${(- \frac{2}{5} y^{3})}^{2}$

Step 1

Combine $y^{3}$ and $\frac{2}{5}$ .

${(- \frac{y^{3} \cdot 2}{5})}^{2}$

Step 2

Move $2$ to the left of $y^{3}$ .

${(- \frac{2 \cdot y^{3}}{5})}^{2}$

Step 3

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

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Step 3.1

Apply the product rule to $- \frac{2 y^{3}}{5}$ .

${(- 1)}^{2} {(\frac{2 y^{3}}{5})}^{2}$

Step 3.2

Apply the product rule to $\frac{2 y^{3}}{5}$ .

${(- 1)}^{2} \frac{{(2 y^{3})}^{2}}{5^{2}}$

Step 3.3

Apply the product rule to $2 y^{3}$ .

${(- 1)}^{2} \frac{2^{2} {(y^{3})}^{2}}{5^{2}}$

Step 4

Simplify the expression.

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Step 4.1

Raise $- 1$ to the power of $2$ .

$1 \frac{2^{2} {(y^{3})}^{2}}{5^{2}}$

Step 4.2

Multiply $\frac{2^{2} {(y^{3})}^{2}}{5^{2}}$ by $1$ .

$\frac{2^{2} {(y^{3})}^{2}}{5^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

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

$\frac{4 {(y^{3})}^{2}}{5^{2}}$

Step 5.2

Multiply the exponents in ${(y^{3})}^{2}$ .

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Step 5.2.1

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

$\frac{4 y^{3 \cdot 2}}{5^{2}}$

Step 5.2.2

Multiply $3$ by $2$ .

$\frac{4 y^{6}}{5^{2}}$

Step 6

Raise $5$ to the power of $2$ .

$\frac{4 y^{6}}{25}$