Basic Math Examples

${(3^{- 4})}^{6} \div 3^{24}$

Step 1

Rewrite the division as a fraction.

$\frac{{(3^{- 4})}^{6}}{3^{24}}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply the exponents in ${(3^{- 4})}^{6}$ .

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Step 2.1.1

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

$\frac{3^{- 4 \cdot 6}}{3^{24}}$

Step 2.1.2

Multiply $- 4$ by $6$ .

$\frac{3^{- 24}}{3^{24}}$

Step 2.2

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

$\frac{\frac{1}{3^{24}}}{3^{24}}$

Step 2.3

Raise $3$ to the power of $24$ .

$\frac{\frac{1}{282429536481}}{3^{24}}$

Step 3

Raise $3$ to the power of $24$ .

$\frac{\frac{1}{282429536481}}{282429536481}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{282429536481} \cdot \frac{1}{282429536481}$

Step 5

Multiply $\frac{1}{282429536481} \cdot \frac{1}{282429536481}$ .

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Step 5.1

Multiply $\frac{1}{282429536481}$ by $\frac{1}{282429536481}$ .

$\frac{1}{282429536481 \cdot 282429536481}$

Step 5.2

Multiply $282429536481$ by $282429536481$ .

$\frac{1}{79766443076872509863361}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{79766443076872509863361}$

Decimal Form:

$1.25366001 \cdot 10^{- 23}$