Basic Math Examples

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

Step 1

Move ${(z^{3} y^{- 4})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $4 z^{- 5} y^{4}$ .

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

Step 2.2

Apply the product rule to $z^{3} y^{- 4}$ .

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

Step 2.3

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

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

Step 2.4

Combine $4$ and $\frac{1}{z^{5}}$ .

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

Step 2.5

Apply the product rule to $\frac{4}{z^{5}}$ .

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

Step 2.6

Raise $4$ to the power of $3$ .

$\frac{1}{\frac{64}{{(z^{5})}^{3}} {(y^{4})}^{3} {(z^{3})}^{2} {(y^{- 4})}^{2}}$

Step 2.7

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

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Step 2.7.1

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

$\frac{1}{\frac{64}{z^{5 \cdot 3}} {(y^{4})}^{3} {(z^{3})}^{2} {(y^{- 4})}^{2}}$

Step 2.7.2

Multiply $5$ by $3$ .

$\frac{1}{\frac{64}{z^{15}} {(y^{4})}^{3} {(z^{3})}^{2} {(y^{- 4})}^{2}}$

Step 2.8

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

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Step 2.8.1

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

$\frac{1}{\frac{64}{z^{15}} y^{4 \cdot 3} {(z^{3})}^{2} {(y^{- 4})}^{2}}$

Step 2.8.2

Multiply $4$ by $3$ .

$\frac{1}{\frac{64}{z^{15}} y^{12} {(z^{3})}^{2} {(y^{- 4})}^{2}}$

Step 2.9

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

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Step 2.9.1

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

$\frac{1}{\frac{64}{z^{15}} y^{12} z^{3 \cdot 2} {(y^{- 4})}^{2}}$

Step 2.9.2

Multiply $3$ by $2$ .

$\frac{1}{\frac{64}{z^{15}} y^{12} z^{6} {(y^{- 4})}^{2}}$

Step 2.10

Multiply the exponents in ${(y^{- 4})}^{2}$ .

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Step 2.10.1

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

$\frac{1}{\frac{64}{z^{15}} y^{12} z^{6} y^{- 4 \cdot 2}}$

Step 2.10.2

Multiply $- 4$ by $2$ .

$\frac{1}{\frac{64}{z^{15}} y^{12} z^{6} y^{- 8}}$

Step 2.11

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

$\frac{1}{\frac{64}{z^{15}} y^{12} z^{6} \frac{1}{y^{8}}}$

Step 2.12

Combine exponents.

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Step 2.12.1

Combine $\frac{64}{z^{15}}$ and $y^{12}$ .

$\frac{1}{\frac{64 y^{12}}{z^{15}} z^{6} \frac{1}{y^{8}}}$

Step 2.12.2

Combine $\frac{64 y^{12}}{z^{15}}$ and $z^{6}$ .

$\frac{1}{\frac{64 y^{12} z^{6}}{z^{15}} \cdot \frac{1}{y^{8}}}$

Step 2.12.3

Multiply $\frac{64 y^{12} z^{6}}{z^{15}}$ by $\frac{1}{y^{8}}$ .

$\frac{1}{\frac{64 y^{12} z^{6}}{z^{15} y^{8}}}$

Step 2.13

Reduce the expression $\frac{64 y^{12} z^{6}}{z^{15} y^{8}}$ by cancelling the common factors.

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Step 2.13.1

Factor $y^{8}$ out of $64 y^{12} z^{6}$ .

$\frac{1}{\frac{y^{8} (64 y^{4} z^{6})}{z^{15} y^{8}}}$

Step 2.13.2

Factor $y^{8}$ out of $z^{15} y^{8}$ .

$\frac{1}{\frac{y^{8} (64 y^{4} z^{6})}{y^{8} z^{15}}}$

Step 2.13.3

Cancel the common factor.

$\frac{1}{\frac{y^{8} (64 y^{4} z^{6})}{y^{8} z^{15}}}$

Step 2.13.4

Rewrite the expression.

$\frac{1}{\frac{64 y^{4} z^{6}}{z^{15}}}$

Step 2.14

Cancel the common factor of $z^{6}$ and $z^{15}$ .

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Step 2.14.1

Factor $z^{6}$ out of $64 y^{4} z^{6}$ .

$\frac{1}{\frac{z^{6} (64 y^{4})}{z^{15}}}$

Step 2.14.2

Cancel the common factors.

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Step 2.14.2.1

Factor $z^{6}$ out of $z^{15}$ .

$\frac{1}{\frac{z^{6} (64 y^{4})}{z^{6} z^{9}}}$

Step 2.14.2.2

Cancel the common factor.

$\frac{1}{\frac{z^{6} (64 y^{4})}{z^{6} z^{9}}}$

Step 2.14.2.3

Rewrite the expression.

$\frac{1}{\frac{64 y^{4}}{z^{9}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{z^{9}}{64 y^{4}}$

Step 4

Multiply $\frac{z^{9}}{64 y^{4}}$ by $1$ .

$\frac{z^{9}}{64 y^{4}}$