Algebra Examples

$\frac{(7.2 \cdot 10^{- 8}) (9.9 \cdot 10^{3})}{(1.2 \cdot 10^{4}) (3 \cdot 10^{- 2})}$

Step 1

Multiply $7.2$ by $9.9$ .

$\frac{71.28 (10^{- 8} \cdot 10^{3})}{(1.2 \cdot 10^{4}) (3 \cdot 10^{- 2})}$

Step 2

Multiply $10^{- 8}$ by $10^{3}$ by adding the exponents.

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Step 2.1

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

$\frac{71.28 \cdot 10^{- 8 + 3}}{(1.2 \cdot 10^{4}) (3 \cdot 10^{- 2})}$

Step 2.2

Add $- 8$ and $3$ .

$\frac{71.28 \cdot 10^{- 5}}{(1.2 \cdot 10^{4}) (3 \cdot 10^{- 2})}$

Step 3

Multiply $1.2$ by $3$ .

$\frac{71.28 \cdot 10^{- 5}}{3.6 (10^{4} \cdot 10^{- 2})}$

Step 4

Multiply $10^{4}$ by $10^{- 2}$ by adding the exponents.

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Step 4.1

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

$\frac{71.28 \cdot 10^{- 5}}{3.6 \cdot 10^{4 - 2}}$

Step 4.2

Subtract $2$ from $4$ .

$\frac{71.28 \cdot 10^{- 5}}{3.6 \cdot 10^{2}}$

Step 5

Divide using scientific notation.

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Step 5.1

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

$(\frac{71.28}{3.6}) (\frac{10^{- 5}}{10^{2}})$

Step 5.2

Divide $71.28$ by $3.6$ .

$19.8 \frac{10^{- 5}}{10^{2}}$

Step 5.3

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

$19.8 \cdot 10^{- 5 + 2 \cdot - 1}$

Step 5.4

Multiply $2$ by $- 1$ .

$19.8 \cdot 10^{- 5 - 2}$

Step 5.5

Subtract $2$ from $- 5$ .

$19.8 \cdot 10^{- 7}$

Step 6

Move the decimal point in $19.8$ to the left by $1$ place and increase the power of $10^{- 7}$ by $1$ .

$1.98 \cdot 10^{- 6}$