Algebra Examples

${(10^{- 5})}^{3} {(9.9 \cdot 10^{- 12})}^{2}$

Step 1

Multiply the exponents in ${(10^{- 5})}^{3}$ .

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Step 1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10^{- 5 \cdot 3} {(9.9 \cdot 10^{- 12})}^{2}$

Step 1.2

Multiply $- 5$ by $3$ .

$10^{- 15} {(9.9 \cdot 10^{- 12})}^{2}$

Step 2

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

$\frac{1}{10^{15}} {(9.9 \cdot 10^{- 12})}^{2}$

Step 3

Raise $10$ to the power of $15$ .

$\frac{1}{1000000000000000} {(9.9 \cdot 10^{- 12})}^{2}$

Step 4

Apply the product rule to $9.9 \cdot 10^{- 12}$ .

$\frac{1}{1000000000000000} ({9.9}^{2} \cdot {(10^{- 12})}^{2})$

Step 5

Raise $9.9$ to the power of $2$ .

$\frac{1}{1000000000000000} (98.01 \cdot {(10^{- 12})}^{2})$

Step 6

Multiply the exponents in ${(10^{- 12})}^{2}$ .

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Step 6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{1000000000000000} (98.01 \cdot 10^{- 12 \cdot 2})$

Step 6.2

Multiply $- 12$ by $2$ .

$\frac{1}{1000000000000000} \cdot 98.01 \cdot 10^{- 24}$

Step 7

Move the decimal point in $98.01$ to the left by $1$ place and increase the power of $10^{- 24}$ by $1$ .

$\frac{1}{1000000000000000} \cdot 9.801 \cdot 10^{- 23}$

Step 8

Multiply $\frac{1}{1000000000000000} \cdot 9.801 \cdot 10^{- 23}$ .

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Step 8.1

Combine $9.801$ and $\frac{1}{1000000000000000}$ .

$\frac{9.801}{1000000000000000} \cdot 10^{- 23}$

Step 8.2

Combine $\frac{9.801}{1000000000000000}$ and $10^{- 23}$ .

$\frac{9.801 \cdot 10^{- 23}}{1000000000000000}$

Step 9

Divide using scientific notation.

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Step 9.1

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

$(\frac{9.801}{1000000000000000}) (\frac{10^{- 23}}{1})$

Step 9.2

Divide $9.801$ by $1000000000000000$ .

$0 \frac{10^{- 23}}{1}$

Step 9.3

Divide $10^{- 23}$ by $1$ .

$0 \cdot 10^{- 23}$

Step 10

Move the decimal point in $0$ to the right by $15$ places and decrease the power of $10^{- 23}$ by $15$ .

$9.801 \cdot 10^{- 38}$