Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Combine.

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

Step 4

Multiply $1$ by $1$ .

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

Step 5

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

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

Step 6

Combine.

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

Step 7

Multiply $1$ by $1$ .

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

Step 8

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

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Step 8.1

Apply the product rule to $\frac{1}{2 x^{3} y^{3}}$ .

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

Step 8.2

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

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

Step 8.3

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

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

Step 9

One to any power is one.

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

Step 10

Simplify the denominator.

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Step 10.1

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

$\frac{1}{32 {(x^{3})}^{5} {(y^{3})}^{5}}$

Step 10.2

Multiply the exponents in ${(x^{3})}^{5}$ .

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Step 10.2.1

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

$\frac{1}{32 x^{3 \cdot 5} {(y^{3})}^{5}}$

Step 10.2.2

Multiply $3$ by $5$ .

$\frac{1}{32 x^{15} {(y^{3})}^{5}}$

Step 10.3

Multiply the exponents in ${(y^{3})}^{5}$ .

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Step 10.3.1

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

$\frac{1}{32 x^{15} y^{3 \cdot 5}}$

Step 10.3.2

Multiply $3$ by $5$ .

$\frac{1}{32 x^{15} y^{15}}$