Trigonometry Examples

${(- 7 x^{- 3} y^{5})}^{- 2}$

Step 1

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

${(- 7 \frac{1}{x^{3}} y^{5})}^{- 2}$

Step 2

Combine $- 7$ and $\frac{1}{x^{3}}$ .

${(\frac{- 7}{x^{3}} y^{5})}^{- 2}$

Step 3

Move the negative in front of the fraction.

${(- \frac{7}{x^{3}} y^{5})}^{- 2}$

Step 4

Combine $y^{5}$ and $\frac{7}{x^{3}}$ .

${(- \frac{y^{5} \cdot 7}{x^{3}})}^{- 2}$

Step 5

Move $7$ to the left of $y^{5}$ .

${(- \frac{7 \cdot y^{5}}{x^{3}})}^{- 2}$

Step 6

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

${(- \frac{x^{3}}{7 y^{5}})}^{2}$

Step 7

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

Tap for more steps...

Step 7.1

Apply the product rule to $- \frac{x^{3}}{7 y^{5}}$ .

${(- 1)}^{2} {(\frac{x^{3}}{7 y^{5}})}^{2}$

Step 7.2

Apply the product rule to $\frac{x^{3}}{7 y^{5}}$ .

${(- 1)}^{2} \frac{{(x^{3})}^{2}}{{(7 y^{5})}^{2}}$

Step 7.3

Apply the product rule to $7 y^{5}$ .

${(- 1)}^{2} \frac{{(x^{3})}^{2}}{7^{2} {(y^{5})}^{2}}$

Step 8

Simplify the expression.

Tap for more steps...

Step 8.1

Raise $- 1$ to the power of $2$ .

$1 \frac{{(x^{3})}^{2}}{7^{2} {(y^{5})}^{2}}$

Step 8.2

Multiply $\frac{{(x^{3})}^{2}}{7^{2} {(y^{5})}^{2}}$ by $1$ .

$\frac{{(x^{3})}^{2}}{7^{2} {(y^{5})}^{2}}$

Step 8.3

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

Tap for more steps...

Step 8.3.1

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

$\frac{x^{3 \cdot 2}}{7^{2} {(y^{5})}^{2}}$

Step 8.3.2

Multiply $3$ by $2$ .

$\frac{x^{6}}{7^{2} {(y^{5})}^{2}}$

Step 9

Simplify the denominator.

Tap for more steps...

Step 9.1

Raise $7$ to the power of $2$ .

$\frac{x^{6}}{49 {(y^{5})}^{2}}$

Step 9.2

Multiply the exponents in ${(y^{5})}^{2}$ .

Tap for more steps...

Step 9.2.1

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

$\frac{x^{6}}{49 y^{5 \cdot 2}}$

Step 9.2.2

Multiply $5$ by $2$ .

$\frac{x^{6}}{49 y^{10}}$