Basic Math Examples

$\frac{(7.6 \cdot 10^{- 174}) (6.9 \cdot 10^{158})}{1.9 \cdot 10^{135}}$

Step 1

Multiply $7.6$ by $6.9$ .

$\frac{52.44 (10^{- 174} \cdot 10^{158})}{1.9 \cdot 10^{135}}$

Step 2

Multiply $10^{- 174}$ by $10^{158}$ 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.

$\frac{52.44 \cdot 10^{- 174 + 158}}{1.9 \cdot 10^{135}}$

Step 2.2

Add $- 174$ and $158$ .

$\frac{52.44 \cdot 10^{- 16}}{1.9 \cdot 10^{135}}$

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.

$(\frac{52.44}{1.9}) (\frac{10^{- 16}}{10^{135}})$

Step 3.2

Divide $52.44$ by $1.9$ .

$27.6 \frac{10^{- 16}}{10^{135}}$

Step 3.3

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

$27.6 \cdot 10^{- 16 + 135 \cdot - 1}$

Step 3.4

Multiply $135$ by $- 1$ .

$27.6 \cdot 10^{- 16 - 135}$

Step 3.5

Subtract $135$ from $- 16$ .

$27.6 \cdot 10^{- 151}$

Step 4

Move the decimal point in $27.6$ to the left by $1$ place and increase the power of $10^{- 151}$ by $1$ .

$2.76 \cdot 10^{- 150}$