Simplify (9*10^-3)^2

${(9 \cdot 10^{- 3})}^{2}$

Step 1

Apply the product rule to $9 \cdot 10^{- 3}$ .

$9^{2} \cdot {(10^{- 3})}^{2}$

Step 2

Raise $9$ to the power of $2$ .

$81 \cdot {(10^{- 3})}^{2}$

Step 3

Multiply the exponents in ${(10^{- 3})}^{2}$ .

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

$81 \cdot 10^{- 3 \cdot 2}$

Multiply $- 3$ by $2$ .

$81 \cdot 10^{- 6}$

Step 4

Move the decimal point in $81$ to the left by $1$ place and increase the power of $10^{- 6}$ by $1$ .

$8.1 \cdot 10^{- 5}$