Trigonometry Examples

${(A^{\frac{9}{4}} \div A^{\frac{3}{4}})}^{- 5}$

Step 1

Move $A^{\frac{3}{4}}$ to the numerator using the negative exponent rule $\frac{1}{i^{n}} = i^{- n}$ .

${(A^{\frac{9}{4}} A^{- \frac{3}{4}})}^{- 5}$

Step 2

Multiply $A^{\frac{9}{4}}$ by $A^{- \frac{3}{4}}$ by adding the exponents.

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Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(A^{\frac{9}{4} - \frac{3}{4}})}^{- 5}$

Step 2.2

Combine the numerators over the common denominator.

${(A^{\frac{9 - 3}{4}})}^{- 5}$

Step 2.3

Subtract $3$ from $9$ .

${(A^{\frac{6}{4}})}^{- 5}$

Step 2.4

Cancel the common factor of $6$ and $4$ .

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Step 2.4.1

Factor $2$ out of $6$ .

${(A^{\frac{2 (3)}{4}})}^{- 5}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $4$ .

${(A^{\frac{2 \cdot 3}{2 \cdot 2}})}^{- 5}$

Step 2.4.2.2

Cancel the common factor.

${(A^{\frac{2 \cdot 3}{2 \cdot 2}})}^{- 5}$

Step 2.4.2.3

Rewrite the expression.

${(A^{\frac{3}{2}})}^{- 5}$