Algebra Examples

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

Step 1

Multiply the exponents in ${(x^{- 4})}^{5}$ .

Tap for more steps...

Step 1.1

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

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

Step 1.2

Multiply $- 4$ by $5$ .

$x^{- 20} {(x^{3} y^{2})}^{5}$

Step 2

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

$\frac{1}{x^{20}} {(x^{3} y^{2})}^{5}$

Step 3

Apply basic rules of exponents.

Tap for more steps...

Step 3.1

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

$\frac{1}{x^{20}} ({(x^{3})}^{5} {(y^{2})}^{5})$

Step 3.2

Multiply the exponents in ${(x^{3})}^{5}$ .

Tap for more steps...

Step 3.2.1

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

$\frac{1}{x^{20}} (x^{3 \cdot 5} {(y^{2})}^{5})$

Step 3.2.2

Multiply $3$ by $5$ .

$\frac{1}{x^{20}} (x^{15} {(y^{2})}^{5})$

Step 4

Cancel the common factor of $x^{15}$ .

Tap for more steps...

Step 4.1

Factor $x^{15}$ out of $x^{20}$ .

$\frac{1}{x^{15} x^{5}} (x^{15} {(y^{2})}^{5})$

Step 4.2

Factor $x^{15}$ out of $x^{15} {(y^{2})}^{5}$ .

$\frac{1}{x^{15} x^{5}} (x^{15} ({(y^{2})}^{5}))$

Step 4.3

Cancel the common factor.

$\frac{1}{x^{15} x^{5}} (x^{15} {(y^{2})}^{5})$

Step 4.4

Rewrite the expression.

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

Step 5

Combine $\frac{1}{x^{5}}$ and ${(y^{2})}^{5}$ .

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

Step 6

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

Tap for more steps...

Step 6.1

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

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

Step 6.2

Multiply $2$ by $5$ .

$\frac{y^{10}}{x^{5}}$