Finite Math Examples

$(6 x \cdot 10^{- 4}) (3 x \cdot 10^{- 6})$

Step 1

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $x$ .

$6 (x \cdot x) \cdot 10^{- 4} \cdot 3 \cdot 10^{- 6}$

Step 1.2

Multiply $x$ by $x$ .

$6 x^{2} \cdot 10^{- 4} \cdot 3 \cdot 10^{- 6}$

Step 2

Multiply $10^{- 4}$ by $10^{- 6}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $10^{- 6}$ .

$6 x^{2} \cdot (10^{- 6} \cdot 10^{- 4}) \cdot 3$

Step 2.2

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

$6 x^{2} \cdot 10^{- 6 - 4} \cdot 3$

Step 2.3

Subtract $4$ from $- 6$ .

$6 x^{2} \cdot 10^{- 10} \cdot 3$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$6 x^{2} \cdot \frac{1}{10^{10}} \cdot 3$

Step 4

Raise $10$ to the power of $10$ .

$6 x^{2} \cdot \frac{1}{10000000000} \cdot 3$

Step 5

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.1

Factor $2$ out of $6 x^{2}$ .

$2 (3 x^{2}) \cdot \frac{1}{10000000000} \cdot 3$

Step 5.2

Factor $2$ out of $10000000000$ .

$2 (3 x^{2}) \cdot \frac{1}{2 (5000000000)} \cdot 3$

Step 5.3

Cancel the common factor.

$2 (3 x^{2}) \cdot \frac{1}{2 \cdot 5000000000} \cdot 3$

Step 5.4

Rewrite the expression.

$3 x^{2} \cdot \frac{1}{5000000000} \cdot 3$

Step 6

Combine $3$ and $\frac{1}{5000000000}$ .

$x^{2} \cdot \frac{3}{5000000000} \cdot 3$

Step 7

Combine $x^{2}$ and $\frac{3}{5000000000}$ .

$\frac{x^{2} \cdot 3}{5000000000} \cdot 3$

Step 8

Move $3$ to the left of $x^{2}$ .

$\frac{3 \cdot x^{2}}{5000000000} \cdot 3$

Step 9

Multiply $\frac{3 x^{2}}{5000000000} \cdot 3$ .

Tap for more steps...

Step 9.1

Combine $\frac{3 x^{2}}{5000000000}$ and $3$ .

$\frac{3 x^{2} \cdot 3}{5000000000}$

Step 9.2

Multiply $3$ by $3$ .

$\frac{9 x^{2}}{5000000000}$