Finite Math Examples

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

Step 1

Multiply $- \frac{1}{3} (x^{2} y)$ .

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Step 1.1

Combine $x^{2}$ and $\frac{1}{3}$ .

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

Step 1.2

Combine $y$ and $\frac{x^{2}}{3}$ .

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

Step 2

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

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

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 $- \frac{3}{y x^{2}}$ .

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

Step 3.2

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

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

Step 3.3

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

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

Step 4

Raise $- 1$ to the power of $3$ .

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

Step 5

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

$- \frac{27}{y^{3} {(x^{2})}^{3}}$

Step 6

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

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Step 6.1

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

$- \frac{27}{y^{3} x^{2 \cdot 3}}$

Step 6.2

Multiply $2$ by $3$ .

$- \frac{27}{y^{3} x^{6}}$