Evaluate ((4*10^3)/(10^-2))^2

${(\frac{4 \cdot 10^{3}}{10^{- 2}})}^{2}$

Step 1

Divide using scientific notation.

Group coefficients together and exponents together to divide numbers in scientific notation.

${((\frac{4}{1}) (\frac{10^{3}}{10^{- 2}}))}^{2}$

Divide $4$ by $1$ .

${(4 \frac{10^{3}}{10^{- 2}})}^{2}$

Subtract the exponent from the denominator from the exponent of the numerator for the same base

${(4 \cdot 10^{3 - 2 \cdot - 1})}^{2}$

Multiply $- 2$ by $- 1$ .

${(4 \cdot 10^{3 + 2})}^{2}$

Add $3$ and $2$ .

${(4 \cdot 10^{5})}^{2}$

Step 2

Apply the product rule to $4 \cdot 10^{5}$ .

$4^{2} \cdot {(10^{5})}^{2}$

Step 3

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

$16 \cdot {(10^{5})}^{2}$

Step 4

Multiply the exponents in ${(10^{5})}^{2}$ .

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

$16 \cdot 10^{5 \cdot 2}$

Multiply $5$ by $2$ .

$16 \cdot 10^{10}$

Step 5

Move the decimal point in $16$ to the left by $1$ place and increase the power of $10^{10}$ by $1$ .

$1.6 \cdot 10^{11}$

Step 6

The result can be shown in multiple forms.

Scientific Notation:

$1.6 \cdot 10^{11}$

Expanded Form:

$160000000000$