Evaluate Using Scientific Notation (4*10^8)^-2

${(4 \cdot 10^{8})}^{- 2}$

Step 1

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

$\frac{1}{{(4 \cdot 10^{8})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $4 \cdot 10^{8}$ .

$\frac{1}{4^{2} \cdot {(10^{8})}^{2}}$

Raise $4$ to the power of $2$ .

$\frac{1}{16 \cdot {(10^{8})}^{2}}$

Multiply the exponents in ${(10^{8})}^{2}$ .

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

$\frac{1}{16 \cdot 10^{8 \cdot 2}}$

Multiply $8$ by $2$ .

$\frac{1}{16 \cdot 10^{16}}$

Raise $10$ to the power of $16$ .

$\frac{1}{16 \cdot 10000000000000000}$

Step 3

Multiply $16$ by $10000000000000000$ .

$\frac{1}{160000000000000000}$