Basic Math Examples

{(1.3 \cdot 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}}

$b^{- n} = \frac{1}{b^{n}}$ .

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

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

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to

1.3 \cdot 10^{- 3}

$1.3 \cdot 10^{- 3}$ .

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

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

Step 2.2

Raise

1.3

$1.3$ to the power of

2

$2$ .

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

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

Step 2.3

Multiply the exponents in

{(10^{- 3})}^{2}

${(10^{- 3})}^{2}$ .

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Step 2.3.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

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

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

Step 2.3.2

Multiply

- 3

$- 3$ by

2

$2$ .

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

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

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

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

Step 2.4

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

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

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

Step 2.5

Raise

10

$10$ to the power of

6

$6$ .

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

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

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

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

Step 3

Combine

1.69

$1.69$ and

\frac{1}{1000000}

$\frac{1}{1000000}$ .

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

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

Step 4

Simplify by dividing numbers.

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Step 4.1

Divide

1.69

$1.69$ by

1000000

$1000000$ .

\frac{1}{0.00000169}

$\frac{1}{0.00000169}$

Step 4.2

Divide

1

$1$ by

0.00000169

$0.00000169$ .

591715.97633136

$591715.97633136$

591715.97633136

$591715.97633136$