Algebra Examples

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

Step 1

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

$\frac{1}{3^{3}} \cdot 10^{- 3}$

Step 2

Raise $3$ to the power of $3$ .

$\frac{1}{27} \cdot 10^{- 3}$

Step 3

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

$\frac{1}{27} \cdot \frac{1}{10^{3}}$

Step 4

Combine.

$\frac{1 \cdot 1}{27 \cdot 10^{3}}$

Step 5

Multiply $1$ by $1$ .

$\frac{1}{27 \cdot 10^{3}}$

Step 6

Divide using scientific notation.

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Step 6.1

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

$(\frac{1}{27}) (\frac{1}{10^{3}})$

Step 6.2

Divide $1$ by $27$ .

$0.\overline{037} \frac{1}{10^{3}}$

Step 6.3

Move $10^{3}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$0.\overline{037} \cdot 10^{- 3}$

Step 7

Move the decimal point in $0.\overline{037}$ to the right by $2$ places and decrease the power of $10^{- 3}$ by $2$ .

$3.\overline{703} \cdot 10^{- 5}$