Basic Math Examples

$\frac{(2.5 \cdot 10^{4}) \cdot 10^{1.5 (6)}}{(2.5 \cdot 10^{4}) \cdot 10^{1.5 (2)}}$

Step 1

Multiply

$10^{4}$ by

$10^{1.5 (6)}$ by adding the exponents.

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Step 1.1

Move

$10^{1.5 (6)}$ .

$\frac{2.5 \cdot (10^{1.5 (6)} \cdot 10^{4})}{(2.5 \cdot 10^{4}) \cdot 10^{1.5 (2)}}$

Step 1.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2.5 \cdot 10^{1.5 (6) + 4}}{(2.5 \cdot 10^{4}) \cdot 10^{1.5 (2)}}$

Step 1.3

Multiply

$1.5$ by

$6$ .

$\frac{2.5 \cdot 10^{9 + 4}}{(2.5 \cdot 10^{4}) \cdot 10^{1.5 (2)}}$

Step 1.4

Add

$9$ and

$4$ .

$\frac{2.5 \cdot 10^{13}}{(2.5 \cdot 10^{4}) \cdot 10^{1.5 (2)}}$

Step 2

Multiply

$10^{4}$ by

$10^{1.5 (2)}$ by adding the exponents.

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Step 2.1

Move

$10^{1.5 (2)}$ .

$\frac{2.5 \cdot 10^{13}}{2.5 \cdot (10^{1.5 (2)} \cdot 10^{4})}$

Step 2.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2.5 \cdot 10^{13}}{2.5 \cdot 10^{1.5 (2) + 4}}$

Step 2.3

Multiply

$1.5$ by

$2$ .

$\frac{2.5 \cdot 10^{13}}{2.5 \cdot 10^{3 + 4}}$

Step 2.4

Add

$3$ and

$4$ .

$\frac{2.5 \cdot 10^{13}}{2.5 \cdot 10^{7}}$

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.

$(\frac{2.5}{2.5}) (\frac{10^{13}}{10^{7}})$

Step 3.2

Divide

$2.5$ by

$2.5$ .

$1 \frac{10^{13}}{10^{7}}$

Step 3.3

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

$1 \cdot 10^{13 + 7 \cdot - 1}$

Step 3.4

Multiply

$7$ by

$- 1$ .

$1 \cdot 10^{13 - 7}$

Step 3.5

Subtract

$7$ from

$13$ .

$1 \cdot 10^{6}$

Step 4

Multiply

$10^{6}$ by

$1$ .

$10^{6}$

Step 5

Raise

$10$ to the power of

$6$ .

$1000000$