Evaluate Using Scientific Notation (2*10^13)^-2

${(2 \cdot 10^{13})}^{- 2}$

Step 1

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

$\frac{1}{{(2 \cdot 10^{13})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $2 \cdot 10^{13}$ .

$\frac{1}{2^{2} \cdot {(10^{13})}^{2}}$

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

$\frac{1}{4 \cdot {(10^{13})}^{2}}$

Multiply the exponents in ${(10^{13})}^{2}$ .

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

$\frac{1}{4 \cdot 10^{13 \cdot 2}}$

Multiply $13$ by $2$ .

$\frac{1}{4 \cdot 10^{26}}$

Raise $10$ to the power of $26$ .

$\frac{1}{4 \cdot 100000000000000000000000000}$

Step 3

Multiply $4$ by $100000000000000000000000000$ .

$\frac{1}{400000000000000000000000000}$