Algebra Examples

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

Step 1

Move $x^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Multiply $x^{- 1}$ by $x^{4}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $x^{4}$ .

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

Step 2.2

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

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

Step 2.3

Subtract $1$ from $4$ .

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

Step 3

Cancel the common factor of $6$ and $2$ .

Tap for more steps...

Step 3.1

Factor $2$ out of $6 y^{3}$ .

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

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $y^{3}$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Simplify the expression.

Tap for more steps...

Step 5.1

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

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

Step 5.2

Raise $3$ to the power of $2$ .

$\frac{9}{{(x^{3})}^{2}}$

Step 5.3

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

Tap for more steps...

Step 5.3.1

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

$\frac{9}{x^{3 \cdot 2}}$

Step 5.3.2

Multiply $3$ by $2$ .

$\frac{9}{x^{6}}$