Simplify (x^-4)^5(x^3y^2)^5

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

Step 1

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

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

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

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.

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

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

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

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

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

Multiply $3$ by $5$ .

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

Step 4

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

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

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

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

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

Cancel the common factor.

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

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 ${(y^{2})}^{5}$ .

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

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

Multiply $2$ by $5$ .

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