Basic Math Examples

$\frac{1}{2} \cdot (9 \cdot 10^{- 31}) \cdot {(3 \cdot 10^{- 17})}^{2}$

Step 1

Multiply $\frac{1}{2} (9 \cdot 10^{- 31})$ .

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Step 1.1

Combine $9$ and $\frac{1}{2}$ .

$\frac{9}{2} \cdot 10^{- 31} \cdot {(3 \cdot 10^{- 17})}^{2}$

Step 1.2

Combine $\frac{9}{2}$ and $10^{- 31}$ .

$\frac{9 \cdot 10^{- 31}}{2} \cdot {(3 \cdot 10^{- 17})}^{2}$

Step 2

Divide using scientific notation.

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Step 2.1

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

$(\frac{9}{2}) (\frac{10^{- 31}}{1}) \cdot {(3 \cdot 10^{- 17})}^{2}$

Step 2.2

Divide $9$ by $2$ .

$4.5 \frac{10^{- 31}}{1} \cdot {(3 \cdot 10^{- 17})}^{2}$

Step 2.3

Divide $10^{- 31}$ by $1$ .

$4.5 \cdot 10^{- 31} \cdot {(3 \cdot 10^{- 17})}^{2}$

Step 3

Apply the product rule to $3 \cdot 10^{- 17}$ .

$4.5 \cdot 10^{- 31} \cdot (3^{2} \cdot {(10^{- 17})}^{2})$

Step 4

Raise $3$ to the power of $2$ .

$4.5 \cdot 10^{- 31} \cdot (9 \cdot {(10^{- 17})}^{2})$

Step 5

Multiply the exponents in ${(10^{- 17})}^{2}$ .

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Step 5.1

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

$4.5 \cdot 10^{- 31} \cdot (9 \cdot 10^{- 17 \cdot 2})$

Step 5.2

Multiply $- 17$ by $2$ .

$4.5 \cdot 10^{- 31} \cdot 9 \cdot 10^{- 34}$

Step 6

Multiply $4.5$ by $9$ .

$40.5 (10^{- 31} \cdot 10^{- 34})$

Step 7

Multiply $10^{- 31}$ by $10^{- 34}$ by adding the exponents.

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Step 7.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$40.5 \cdot 10^{- 31 - 34}$

Step 7.2

Subtract $34$ from $- 31$ .

$40.5 \cdot 10^{- 65}$

Step 8

Move the decimal point in $40.5$ to the left by $1$ place and increase the power of $10^{- 65}$ by $1$ .

$4.05 \cdot 10^{- 64}$