Algebra Examples

${(3 x^{- 4})}^{2} (5 x^{- 2})$

Step 1

Rewrite using the commutative property of multiplication.

$5 {(3 x^{- 4})}^{2} x^{- 2}$

Step 2

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

$5 {(3 \frac{1}{x^{4}})}^{2} x^{- 2}$

Step 3

Combine $3$ and $\frac{1}{x^{4}}$ .

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

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Apply the product rule to $\frac{3}{x^{4}}$ .

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

Step 4.2

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

$5 \frac{9}{{(x^{4})}^{2}} x^{- 2}$

Step 4.3

Multiply the exponents in ${(x^{4})}^{2}$ .

Tap for more steps...

Step 4.3.1

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

$5 \frac{9}{x^{4 \cdot 2}} x^{- 2}$

Step 4.3.2

Multiply $4$ by $2$ .

$5 \frac{9}{x^{8}} x^{- 2}$

Step 5

Multiply $5 \frac{9}{x^{8}}$ .

Tap for more steps...

Step 5.1

Combine $5$ and $\frac{9}{x^{8}}$ .

$\frac{5 \cdot 9}{x^{8}} x^{- 2}$

Step 5.2

Multiply $5$ by $9$ .

$\frac{45}{x^{8}} x^{- 2}$

Step 6

Cancel the common factor of $x^{- 2}$ .

Tap for more steps...

Step 6.1

Factor $x^{- 2}$ out of $x^{8}$ .

$\frac{45}{x^{- 2} x^{10}} x^{- 2}$

Step 6.2

Cancel the common factor.

$\frac{45}{x^{- 2} x^{10}} x^{- 2}$

Step 6.3

Rewrite the expression.

$\frac{45}{x^{10}}$