Evaluate (1.3*10^-3)^-2

${(1.3 \cdot 10^{- 3})}^{- 2}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(1.3 \cdot 10^{- 3})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $1.3 \cdot 10^{- 3}$ .

$\frac{1}{{1.3}^{2} \cdot {(10^{- 3})}^{2}}$

Raise $1.3$ to the power of $2$ .

$\frac{1}{1.69 \cdot {(10^{- 3})}^{2}}$

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

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

$\frac{1}{1.69 \cdot 10^{- 3 \cdot 2}}$

Multiply $- 3$ by $2$ .

$\frac{1}{1.69 \cdot 10^{- 6}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{1.69 \cdot \frac{1}{10^{6}}}$

Raise $10$ to the power of $6$ .

$\frac{1}{1.69 \cdot \frac{1}{1000000}}$

Step 3

Combine $1.69$ and $\frac{1}{1000000}$ .

$\frac{1}{\frac{1.69}{1000000}}$

Step 4

Simplify by dividing numbers.

Divide $1.69$ by $1000000$ .

$\frac{1}{0.00000169}$

Divide $1$ by $0.00000169$ .

$591715.97633136$