Algebra Examples

${(- 4 x^{- 3} y^{- 5})}^{2}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(- 4 \frac{1}{x^{3}} y^{- 5})}^{2}$

Step 2

Combine $- 4$ and $\frac{1}{x^{3}}$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(- \frac{4}{x^{3}} \cdot \frac{1}{y^{5}})}^{2}$

Step 5

Multiply $\frac{1}{y^{5}}$ by $\frac{4}{x^{3}}$ .

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

Step 6

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

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Step 6.1

Apply the product rule to $- \frac{4}{y^{5} x^{3}}$ .

${(- 1)}^{2} {(\frac{4}{y^{5} x^{3}})}^{2}$

Step 6.2

Apply the product rule to $\frac{4}{y^{5} x^{3}}$ .

${(- 1)}^{2} \frac{4^{2}}{{(y^{5} x^{3})}^{2}}$

Step 6.3

Apply the product rule to $y^{5} x^{3}$ .

${(- 1)}^{2} \frac{4^{2}}{{(y^{5})}^{2} {(x^{3})}^{2}}$

Step 7

Simplify the expression.

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Step 7.1

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

$1 \frac{4^{2}}{{(y^{5})}^{2} {(x^{3})}^{2}}$

Step 7.2

Multiply $\frac{4^{2}}{{(y^{5})}^{2} {(x^{3})}^{2}}$ by $1$ .

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

Step 7.3

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

$\frac{16}{{(y^{5})}^{2} {(x^{3})}^{2}}$

Step 8

Simplify the denominator.

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Step 8.1

Multiply the exponents in ${(y^{5})}^{2}$ .

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Step 8.1.1

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

$\frac{16}{y^{5 \cdot 2} {(x^{3})}^{2}}$

Step 8.1.2

Multiply $5$ by $2$ .

$\frac{16}{y^{10} {(x^{3})}^{2}}$

Step 8.2

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

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Step 8.2.1

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

$\frac{16}{y^{10} x^{3 \cdot 2}}$

Step 8.2.2

Multiply $3$ by $2$ .

$\frac{16}{y^{10} x^{6}}$