Basic Math Examples

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

Step 1

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

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

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

$y z^{3} {(\frac{3 z^{2} u}{y^{2}})}^{2}$

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 $\frac{3 z^{2} u}{y^{2}}$ .

$y z^{3} \frac{{(3 z^{2} u)}^{2}}{{(y^{2})}^{2}}$

Step 3.2

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

$y z^{3} \frac{{(3 z^{2})}^{2} u^{2}}{{(y^{2})}^{2}}$

Step 3.3

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

$y z^{3} \frac{3^{2} {(z^{2})}^{2} u^{2}}{{(y^{2})}^{2}}$

Step 4

Simplify the numerator.

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Step 4.1

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

$y z^{3} \frac{9 {(z^{2})}^{2} u^{2}}{{(y^{2})}^{2}}$

Step 4.2

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

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Step 4.2.1

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

$y z^{3} \frac{9 z^{2 \cdot 2} u^{2}}{{(y^{2})}^{2}}$

Step 4.2.2

Multiply $2$ by $2$ .

$y z^{3} \frac{9 z^{4} u^{2}}{{(y^{2})}^{2}}$

Step 5

Simplify terms.

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Step 5.1

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

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Step 5.1.1

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

$y z^{3} \frac{9 z^{4} u^{2}}{y^{2 \cdot 2}}$

Step 5.1.2

Multiply $2$ by $2$ .

$y z^{3} \frac{9 z^{4} u^{2}}{y^{4}}$

Step 5.2

Cancel the common factor of $y$ .

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Step 5.2.1

Factor $y$ out of $y z^{3}$ .

$y (z^{3}) \frac{9 z^{4} u^{2}}{y^{4}}$

Step 5.2.2

Factor $y$ out of $y^{4}$ .

$y (z^{3}) \frac{9 z^{4} u^{2}}{y \cdot y^{3}}$

Step 5.2.3

Cancel the common factor.

$y z^{3} \frac{9 z^{4} u^{2}}{y \cdot y^{3}}$

Step 5.2.4

Rewrite the expression.

$z^{3} \frac{9 z^{4} u^{2}}{y^{3}}$

Step 5.3

Combine $z^{3}$ and $\frac{9 z^{4} u^{2}}{y^{3}}$ .

$\frac{z^{3} (9 z^{4} u^{2})}{y^{3}}$

Step 6

Multiply $z^{3}$ by $z^{4}$ by adding the exponents.

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Step 6.1

Move $z^{4}$ .

$\frac{z^{4} z^{3} (9 u^{2})}{y^{3}}$

Step 6.2

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

$\frac{z^{4 + 3} (9 u^{2})}{y^{3}}$

Step 6.3

Add $4$ and $3$ .

$\frac{z^{7} (9 u^{2})}{y^{3}}$

Step 7

Move $9$ to the left of $z^{7}$ .

$\frac{9 z^{7} u^{2}}{y^{3}}$