Basic Math Examples

$\frac{\frac{1}{{(3.6 \cdot 10^{- 4})}^{3}}}{\frac{1}{{(6 \cdot 10^{3})}^{3}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{{(3.6 \cdot 10^{- 4})}^{3}} {(6 \cdot 10^{3})}^{3}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $3.6 \cdot 10^{- 4}$ .

$\frac{1}{{3.6}^{3} \cdot {(10^{- 4})}^{3}} {(6 \cdot 10^{3})}^{3}$

Step 2.2

Raise $3.6$ to the power of $3$ .

$\frac{1}{46.656 \cdot {(10^{- 4})}^{3}} {(6 \cdot 10^{3})}^{3}$

Step 2.3

Multiply the exponents in ${(10^{- 4})}^{3}$ .

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Step 2.3.1

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

$\frac{1}{46.656 \cdot 10^{- 4 \cdot 3}} {(6 \cdot 10^{3})}^{3}$

Step 2.3.2

Multiply $- 4$ by $3$ .

$\frac{1}{46.656 \cdot 10^{- 12}} {(6 \cdot 10^{3})}^{3}$

Step 2.4

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

$\frac{1}{46.656 \cdot \frac{1}{10^{12}}} {(6 \cdot 10^{3})}^{3}$

Step 2.5

Raise $10$ to the power of $12$ .

$\frac{1}{46.656 \cdot \frac{1}{1000000000000}} {(6 \cdot 10^{3})}^{3}$

Step 3

Combine $46.656$ and $\frac{1}{1000000000000}$ .

$\frac{1}{\frac{46.656}{1000000000000}} {(6 \cdot 10^{3})}^{3}$

Step 4

Divide $46.656$ by $1000000000000$ .

$\frac{1}{0} {(6 \cdot 10^{3})}^{3}$

Step 5

The expression contains a division by $0$ . The expression is undefined.

Undefined