Finite Math Examples

${(\frac{2 x y^{3}}{z^{- 1}})}^{- 3} (y^{- 3} z^{7})$

Step 1

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

${(2 x y^{3} z)}^{- 3} (y^{- 3} z^{7})$

Step 2

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

$\frac{1}{{(2 x y^{3} z)}^{3}} (y^{- 3} z^{7})$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{1}{{(2 x y^{3})}^{3} z^{3}} (y^{- 3} z^{7})$

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 $2 x y^{3}$ .

$\frac{1}{{(2 x)}^{3} {(y^{3})}^{3} z^{3}} (y^{- 3} z^{7})$

Step 3.2.2

Apply the product rule to $2 x$ .

$\frac{1}{2^{3} x^{3} {(y^{3})}^{3} z^{3}} (y^{- 3} z^{7})$

Step 3.3

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

$\frac{1}{8 x^{3} {(y^{3})}^{3} z^{3}} (y^{- 3} z^{7})$

Step 3.4

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

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Step 3.4.1

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

$\frac{1}{8 x^{3} y^{3 \cdot 3} z^{3}} (y^{- 3} z^{7})$

Step 3.4.2

Multiply $3$ by $3$ .

$\frac{1}{8 x^{3} y^{9} z^{3}} (y^{- 3} z^{7})$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $y^{- 3} z^{3}$ .

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Step 4.1.1

Factor $y^{- 3} z^{3}$ out of $8 x^{3} y^{9} z^{3}$ .

$\frac{1}{y^{- 3} z^{3} (8 x^{3} y^{12})} (y^{- 3} z^{7})$

Step 4.1.2

Factor $y^{- 3} z^{3}$ out of $y^{- 3} z^{7}$ .

$\frac{1}{y^{- 3} z^{3} (8 x^{3} y^{12})} (y^{- 3} z^{3} (z^{4}))$

Step 4.1.3

Cancel the common factor.

$\frac{1}{y^{- 3} z^{3} (8 x^{3} y^{12})} (y^{- 3} z^{3} z^{4})$

Step 4.1.4

Rewrite the expression.

$\frac{1}{8 x^{3} y^{12}} z^{4}$

Step 4.2

Combine $\frac{1}{8 x^{3} y^{12}}$ and $z^{4}$ .

$\frac{z^{4}}{8 x^{3} y^{12}}$