Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

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

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

Step 5.2

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

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Multiply $3$ by $2$ .

$\frac{y^{6}}{{(x^{2})}^{2} z^{2}}$

Step 7

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

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Step 7.1

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

$\frac{y^{6}}{x^{2 \cdot 2} z^{2}}$

Step 7.2

Multiply $2$ by $2$ .

$\frac{y^{6}}{x^{4} z^{2}}$