Basic Math Examples

$((\frac{4^{- 2}}{4^{3}}) (\frac{2^{2}}{2^{8}})) \cdot 3$

Step 1

Combine.

$\frac{4^{- 2} \cdot 2^{2}}{4^{3} \cdot 2^{8}} \cdot 3$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

$\frac{{(2^{2})}^{- 2} \cdot 2^{2}}{4^{3} \cdot 2^{8}} \cdot 3$

Step 2.2

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

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Step 2.2.1

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

$\frac{2^{2 \cdot - 2} \cdot 2^{2}}{4^{3} \cdot 2^{8}} \cdot 3$

Step 2.2.2

Multiply $2$ by $- 2$ .

$\frac{2^{- 4} \cdot 2^{2}}{4^{3} \cdot 2^{8}} \cdot 3$

Step 2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2^{- 4 + 2}}{4^{3} \cdot 2^{8}} \cdot 3$

Step 2.4

Add $- 4$ and $2$ .

$\frac{2^{- 2}}{4^{3} \cdot 2^{8}} \cdot 3$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $4$ as $2^{2}$ .

$\frac{2^{- 2}}{{(2^{2})}^{3} \cdot 2^{8}} \cdot 3$

Step 3.2

Multiply the exponents in ${(2^{2})}^{3}$ .

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Step 3.2.1

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

$\frac{2^{- 2}}{2^{2 \cdot 3} \cdot 2^{8}} \cdot 3$

Step 3.2.2

Multiply $2$ by $3$ .

$\frac{2^{- 2}}{2^{6} \cdot 2^{8}} \cdot 3$

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2^{- 2}}{2^{6 + 8}} \cdot 3$

Step 3.4

Add $6$ and $8$ .

$\frac{2^{- 2}}{2^{14}} \cdot 3$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{\frac{1}{2^{2}}}{2^{14}} \cdot 3$

Step 4.2

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

$\frac{\frac{1}{4}}{2^{14}} \cdot 3$

Step 5

Raise $2$ to the power of $14$ .

$\frac{\frac{1}{4}}{16384} \cdot 3$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{4} \cdot \frac{1}{16384} \cdot 3$

Step 7

Multiply $\frac{1}{4} \cdot \frac{1}{16384}$ .

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Step 7.1

Multiply $\frac{1}{4}$ by $\frac{1}{16384}$ .

$\frac{1}{4 \cdot 16384} \cdot 3$

Step 7.2

Multiply $4$ by $16384$ .

$\frac{1}{65536} \cdot 3$

Step 8

Combine $\frac{1}{65536}$ and $3$ .

$\frac{3}{65536}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{65536}$

Decimal Form:

$4.57763671 \cdot 10^{- 5}$