Trigonometry Examples

${(\frac{a^{2}}{b^{3}})}^{- 3}$

Step 1

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

${(\frac{b^{3}}{a^{2}})}^{3}$

Step 2

Apply the product rule to $\frac{b^{3}}{a^{2}}$ .

$\frac{{(b^{3})}^{3}}{{(a^{2})}^{3}}$

Step 3

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

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Step 3.1

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

$\frac{b^{3 \cdot 3}}{{(a^{2})}^{3}}$

Step 3.2

Multiply $3$ by $3$ .

$\frac{b^{9}}{{(a^{2})}^{3}}$

Step 4

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

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Step 4.1

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

$\frac{b^{9}}{a^{2 \cdot 3}}$

Step 4.2

Multiply $2$ by $3$ .

$\frac{b^{9}}{a^{6}}$