Basic Math Examples

$\frac{16 \cdot 10^{3}}{5 \cdot 10^{7}} \cdot \frac{15 \cdot 10^{2}}{4 \cdot 10^{5}}$

Step 1

Divide using scientific notation.

Tap for more steps...

Step 1.1

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

$(\frac{16}{5}) (\frac{10^{3}}{10^{7}}) \cdot \frac{15 \cdot 10^{2}}{4 \cdot 10^{5}}$

Step 1.2

Divide $16$ by $5$ .

$3.2 \frac{10^{3}}{10^{7}} \cdot \frac{15 \cdot 10^{2}}{4 \cdot 10^{5}}$

Step 1.3

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

$3.2 \cdot 10^{3 + 7 \cdot - 1} \cdot \frac{15 \cdot 10^{2}}{4 \cdot 10^{5}}$

Step 1.4

Multiply $7$ by $- 1$ .

$3.2 \cdot 10^{3 - 7} \cdot \frac{15 \cdot 10^{2}}{4 \cdot 10^{5}}$

Step 1.5

Subtract $7$ from $3$ .

$3.2 \cdot 10^{- 4} \cdot \frac{15 \cdot 10^{2}}{4 \cdot 10^{5}}$

Step 2

Divide using scientific notation.

Tap for more steps...

Step 2.1

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

$3.2 \cdot 10^{- 4} \cdot ((\frac{15}{4}) (\frac{10^{2}}{10^{5}}))$

Step 2.2

Divide $15$ by $4$ .

$3.2 \cdot 10^{- 4} \cdot (3.75 \frac{10^{2}}{10^{5}})$

Step 2.3

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

$3.2 \cdot 10^{- 4} \cdot (3.75 \cdot 10^{2 + 5 \cdot - 1})$

Step 2.4

Multiply $5$ by $- 1$ .

$3.2 \cdot 10^{- 4} \cdot (3.75 \cdot 10^{2 - 5})$

Step 2.5

Subtract $5$ from $2$ .

$3.2 \cdot 10^{- 4} \cdot 3.75 \cdot 10^{- 3}$

Step 3

Multiply $3.2$ by $3.75$ .

$12 (10^{- 4} \cdot 10^{- 3})$

Step 4

Multiply $10^{- 4}$ by $10^{- 3}$ by adding the exponents.

Tap for more steps...

Step 4.1

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

$12 \cdot 10^{- 4 - 3}$

Step 4.2

Subtract $3$ from $- 4$ .

$12 \cdot 10^{- 7}$

Step 5

Move the decimal point in $12$ to the left by $1$ place and increase the power of $10^{- 7}$ by $1$ .

$1.2 \cdot 10^{- 6}$