Simplify ((x^-5)^2*x^15)/(x^3)

$\frac{{(x^{- 5})}^{2} \cdot x^{15}}{x^{3}}$

Step 1

Cancel the common factor of $x^{15}$ and $x^{3}$ .

Factor $x^{3}$ out of ${(x^{- 5})}^{2} \cdot x^{15}$ .

$\frac{x^{3} ({(x^{- 5})}^{2} \cdot x^{12})}{x^{3}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{x^{3} ({(x^{- 5})}^{2} \cdot x^{12})}{x^{3} \cdot 1}$

Cancel the common factor.

$\frac{x^{3} ({(x^{- 5})}^{2} \cdot x^{12})}{x^{3} \cdot 1}$

Rewrite the expression.

$\frac{{(x^{- 5})}^{2} \cdot x^{12}}{1}$

Divide ${(x^{- 5})}^{2} \cdot x^{12}$ by $1$ .

${(x^{- 5})}^{2} \cdot x^{12}$

Step 2

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

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

$x^{- 5 \cdot 2} \cdot x^{12}$

Multiply $- 5$ by $2$ .

$x^{- 10} \cdot x^{12}$

Step 3

Multiply $x^{- 10}$ by $x^{12}$ by adding the exponents.

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

$x^{- 10 + 12}$

Add $- 10$ and $12$ .

$x^{2}$