Basic Math Examples

${((0.2) (10^{- 3}))}^{- 1} {((2.5) (10^{4}))}^{2}$

Step 1

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

${(0.2 \frac{1}{10^{3}})}^{- 1} {((2.5) (10^{4}))}^{2}$

Step 2

Raise $10$ to the power of $3$ .

${(0.2 (\frac{1}{1000}))}^{- 1} {((2.5) (10^{4}))}^{2}$

Step 3

Cancel the common factor of $0.2$ .

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Step 3.1

Factor $0.2$ out of $1000$ .

${(0.2 \frac{1}{0.2 (5000)})}^{- 1} {((2.5) (10^{4}))}^{2}$

Step 3.2

Cancel the common factor.

${(0.2 \frac{1}{0.2 \cdot 5000})}^{- 1} {((2.5) (10^{4}))}^{2}$

Step 3.3

Rewrite the expression.

${(\frac{1}{5000})}^{- 1} {((2.5) (10^{4}))}^{2}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

$5000 {((2.5) (10^{4}))}^{2}$

Step 5

Raise $10$ to the power of $4$ .

$5000 {(2.5 \cdot 10000)}^{2}$

Step 6

Multiply $2.5$ by $10000$ .

$5000 \cdot 25000^{2}$

Step 7

Raise $25000$ to the power of $2$ .

$5000 \cdot 625000000$

Step 8

Multiply $5000$ by $625000000$ .

$3125000000000$