How do you simplify (d^2)^-4?

May 30, 2018

(d^2)^(-4)=color(blue)(1/d^8

Explanation:

Simplify:

${\left({d}^{2}\right)}^{- 4}$

Apply the power rule of exponents: ${\left({a}^{m}\right)}^{m} = {a}^{m \cdot n}$

${d}^{2 \cdot \left(- 4\right)}$

${d}^{- 8}$

Apply the negative exponent rule: ${a}^{- m} = \frac{1}{a} ^ m$.

${d}^{- 8} = \frac{1}{d} ^ 8$

May 30, 2018

${d}^{-} 8 \mathmr{and} \frac{1}{d} ^ 8$
Because of the power of a power property, you'll want to multiply your exponents. 2 * -4 = -8, so this gives you ${d}^{-} 8$ or, when simplified even further, $\frac{1}{d} ^ 8$.