Simplify (-2(x^-2)^4)/(-2x^-10)

$\frac{- 2 {(x^{- 2})}^{4}}{- 2 x^{- 10}}$

Step 1

Move $x^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 2 {(x^{- 2})}^{4} x^{10}}{- 2}$

Step 2

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 {(x^{- 2})}^{4} x^{10}}{- 2}$

Divide ${(x^{- 2})}^{4} x^{10}$ by $1$ .

${(x^{- 2})}^{4} x^{10}$

Step 3

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

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

$x^{- 2 \cdot 4} x^{10}$

Multiply $- 2$ by $4$ .

$x^{- 8} x^{10}$

Step 4

Multiply $x^{- 8}$ by $x^{10}$ by adding the exponents.

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

$x^{- 8 + 10}$

Add $- 8$ and $10$ .

$x^{2}$