Pre-Algebra Examples

$\frac{(1.5 \cdot 10^{24}) (6 \cdot 10^{- 12})}{2 \cdot 10^{3}}$

Step 1

Multiply $1.5$ by $6$ .

$\frac{9 (10^{24} \cdot 10^{- 12})}{2 \cdot 10^{3}}$

Step 2

Multiply $10^{24}$ by $10^{- 12}$ 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.

$\frac{9 \cdot 10^{24 - 12}}{2 \cdot 10^{3}}$

Step 2.2

Subtract $12$ from $24$ .

$\frac{9 \cdot 10^{12}}{2 \cdot 10^{3}}$

Step 3

Divide using scientific notation.

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Step 3.1

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

$(\frac{9}{2}) (\frac{10^{12}}{10^{3}})$

Step 3.2

Divide $9$ by $2$ .

$4.5 \frac{10^{12}}{10^{3}}$

Step 3.3

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

$4.5 \cdot 10^{12 + 3 \cdot - 1}$

Step 3.4

Multiply $3$ by $- 1$ .

$4.5 \cdot 10^{12 - 3}$

Step 3.5

Subtract $3$ from $12$ .

$4.5 \cdot 10^{9}$

Step 4

The result can be shown in multiple forms.

Scientific Notation:

$4.5 \cdot 10^{9}$

Expanded Form:

$4500000000$