Basic Math Examples

${(\frac{2 w y^{- 4}}{z^{- 3}})}^{3} (w^{2} z^{- 1})$

Step 1

Move $y^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{2 w}{z^{- 3} y^{4}})}^{3} (w^{2} z^{- 1})$

Step 2

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

${(\frac{2 w z^{3}}{y^{4}})}^{3} (w^{2} z^{- 1})$

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 $\frac{2 w z^{3}}{y^{4}}$ .

$\frac{{(2 w z^{3})}^{3}}{{(y^{4})}^{3}} (w^{2} z^{- 1})$

Step 3.2

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

$\frac{{(2 w)}^{3} {(z^{3})}^{3}}{{(y^{4})}^{3}} (w^{2} z^{- 1})$

Step 3.3

Apply the product rule to $2 w$ .

$\frac{2^{3} w^{3} {(z^{3})}^{3}}{{(y^{4})}^{3}} (w^{2} z^{- 1})$

Step 4

Simplify the numerator.

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Step 4.1

Raise $2$ to the power of $3$ .

$\frac{8 w^{3} {(z^{3})}^{3}}{{(y^{4})}^{3}} (w^{2} z^{- 1})$

Step 4.2

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

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Step 4.2.1

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

$\frac{8 w^{3} z^{3 \cdot 3}}{{(y^{4})}^{3}} (w^{2} z^{- 1})$

Step 4.2.2

Multiply $3$ by $3$ .

$\frac{8 w^{3} z^{9}}{{(y^{4})}^{3}} (w^{2} z^{- 1})$

Step 5

Multiply the exponents in ${(y^{4})}^{3}$ .

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Step 5.1

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

$\frac{8 w^{3} z^{9}}{y^{4 \cdot 3}} (w^{2} z^{- 1})$

Step 5.2

Multiply $4$ by $3$ .

$\frac{8 w^{3} z^{9}}{y^{12}} (w^{2} z^{- 1})$

Step 6

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

$\frac{8 w^{3} z^{9}}{y^{12}} (w^{2} \frac{1}{z})$

Step 7

Combine $w^{2}$ and $\frac{1}{z}$ .

$\frac{8 w^{3} z^{9}}{y^{12}} \cdot \frac{w^{2}}{z}$

Step 8

Combine.

$\frac{8 w^{3} z^{9} w^{2}}{y^{12} z}$

Step 9

Multiply $w^{3}$ by $w^{2}$ by adding the exponents.

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Step 9.1

Move $w^{2}$ .

$\frac{8 (w^{2} w^{3}) z^{9}}{y^{12} z}$

Step 9.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{8 w^{2 + 3} z^{9}}{y^{12} z}$

Step 9.3

Add $2$ and $3$ .

$\frac{8 w^{5} z^{9}}{y^{12} z}$

Step 10

Cancel the common factor of $z^{9}$ and $z$ .

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Step 10.1

Factor $z$ out of $8 w^{5} z^{9}$ .

$\frac{z (8 w^{5} z^{8})}{y^{12} z}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $z$ out of $y^{12} z$ .

$\frac{z (8 w^{5} z^{8})}{z y^{12}}$

Step 10.2.2

Cancel the common factor.

$\frac{z (8 w^{5} z^{8})}{z y^{12}}$

Step 10.2.3

Rewrite the expression.

$\frac{8 w^{5} z^{8}}{y^{12}}$