Algebra Examples

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

Step 1

Move $w^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

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

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

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $5 x y^{3} z^{2} w^{3}$ .

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

Step 3.2

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

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Step 3.2.1

Apply the product rule to $5 x y^{3} z^{2}$ .

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

Step 3.2.2

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

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

Step 3.2.3

Apply the product rule to $5 x$ .

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

Step 3.3

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

$\frac{1}{3125 x^{5} {(y^{3})}^{5} {(z^{2})}^{5} {(w^{3})}^{5}}$

Step 3.4

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

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Step 3.4.1

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

$\frac{1}{3125 x^{5} y^{3 \cdot 5} {(z^{2})}^{5} {(w^{3})}^{5}}$

Step 3.4.2

Multiply $3$ by $5$ .

$\frac{1}{3125 x^{5} y^{15} {(z^{2})}^{5} {(w^{3})}^{5}}$

Step 3.5

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

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Step 3.5.1

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

$\frac{1}{3125 x^{5} y^{15} z^{2 \cdot 5} {(w^{3})}^{5}}$

Step 3.5.2

Multiply $2$ by $5$ .

$\frac{1}{3125 x^{5} y^{15} z^{10} {(w^{3})}^{5}}$

Step 3.6

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

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Step 3.6.1

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

$\frac{1}{3125 x^{5} y^{15} z^{10} w^{3 \cdot 5}}$

Step 3.6.2

Multiply $3$ by $5$ .

$\frac{1}{3125 x^{5} y^{15} z^{10} w^{15}}$