Basic Math Examples

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

Step 1

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

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

Step 2

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

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

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

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

Step 3.2

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

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

Step 4

Simplify the numerator.

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

Multiply $3$ by $3$ .

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Multiply $2$ by $3$ .

$\frac{z^{9} y^{6}}{{(b^{4})}^{3}}$

Step 5

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

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Step 5.1

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

$\frac{z^{9} y^{6}}{b^{4 \cdot 3}}$

Step 5.2

Multiply $4$ by $3$ .

$\frac{z^{9} y^{6}}{b^{12}}$