Simplify d(d^-2)^-9

$d {(d^{- 2})}^{- 9}$

Step 1

Multiply the exponents in ${(d^{- 2})}^{- 9}$ .

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

$d \cdot d^{- 2 \cdot - 9}$

Multiply $- 2$ by $- 9$ .

$d \cdot d^{18}$

Step 2

Multiply $d$ by $d^{18}$ by adding the exponents.

Multiply $d$ by $d^{18}$ .

Raise $d$ to the power of $1$ .

$d^{1} d^{18}$

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

$d^{1 + 18}$

Add $1$ and $18$ .

$d^{19}$