Precalculus Examples

${(\frac{6 x^{- 1} y^{4}}{3 x y})}^{- 2}$

Step 1

Move $x^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{6 y^{4}}{3 x y x})}^{- 2}$

Step 2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $x$ .

${(\frac{6 y^{4}}{3 (x \cdot x) y})}^{- 2}$

Step 2.2

Multiply $x$ by $x$ .

${(\frac{6 y^{4}}{3 x^{2} y})}^{- 2}$

Step 3

Cancel the common factor of $6$ and $3$ .

Tap for more steps...

Step 3.1

Factor $3$ out of $6 y^{4}$ .

${(\frac{3 (2 y^{4})}{3 x^{2} y})}^{- 2}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $3$ out of $3 x^{2} y$ .

${(\frac{3 (2 y^{4})}{3 (x^{2} y)})}^{- 2}$

Step 3.2.2

Cancel the common factor.

${(\frac{3 (2 y^{4})}{3 (x^{2} y)})}^{- 2}$

Step 3.2.3

Rewrite the expression.

${(\frac{2 y^{4}}{x^{2} y})}^{- 2}$

Step 4

Cancel the common factor of $y^{4}$ and $y$ .

Tap for more steps...

Step 4.1

Factor $y$ out of $2 y^{4}$ .

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

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $y$ out of $x^{2} y$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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

Step 6

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

Tap for more steps...

Step 6.1

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

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

Step 6.2

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

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

Step 7

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

Tap for more steps...

Step 7.1

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

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

Step 7.2

Multiply $2$ by $2$ .

$\frac{x^{4}}{2^{2} {(y^{3})}^{2}}$

Step 8

Simplify the denominator.

Tap for more steps...

Step 8.1

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

$\frac{x^{4}}{4 {(y^{3})}^{2}}$

Step 8.2

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

Tap for more steps...

Step 8.2.1

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

$\frac{x^{4}}{4 y^{3 \cdot 2}}$

Step 8.2.2

Multiply $3$ by $2$ .

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