Algebra Examples

$\frac{(4.56 \cdot 10^{3}) (2.5 \cdot 10^{2})}{(5.377 \cdot 10^{4})}$

Step 1

Multiply $4.56$ by $2.5$ .

$\frac{11.4 (10^{3} \cdot 10^{2})}{5.377 \cdot 10^{4}}$

Step 2

Multiply $10^{3}$ by $10^{2}$ 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.

$\frac{11.4 \cdot 10^{3 + 2}}{5.377 \cdot 10^{4}}$

Step 2.2

Add $3$ and $2$ .

$\frac{11.4 \cdot 10^{5}}{5.377 \cdot 10^{4}}$

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.

$(\frac{11.4}{5.377}) (\frac{10^{5}}{10^{4}})$

Step 3.2

Divide $11.4$ by $5.377$ .

$2.12014134 \frac{10^{5}}{10^{4}}$

Step 3.3

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

$2.12014134 \cdot 10^{5 + 4 \cdot - 1}$

Step 3.4

Multiply $4$ by $- 1$ .

$2.12014134 \cdot 10^{5 - 4}$

Step 3.5

Subtract $4$ from $5$ .

$2.12014134 \cdot 10^{1}$

Step 4

The result can be shown in multiple forms.

Scientific Notation:

$2.12014134 \cdot 10^{1}$

Expanded Form:

$21.20141342$