Solve (1/4)^11-(1/4)^12/(frac{1{4})^12+(1/4)^13}

$$\frac { ( \frac { 1 } { 4 } ) ^ { 11 } - ( \frac { 1 } { 4 } ) ^ { 12 } } { ( \frac { 1 } { 4 } ) ^ { 12 } + ( \frac { 1 } { 4 } ) ^ { 13 } }$$

Evaluate

$$\frac{12}{5}=2.4$$

Solution Steps

Calculate \frac{1}{4} to the power of 11 and get \frac{1}{4194304}.

$$\frac{\frac{1}{4194304}-\left(\frac{1}{4}\right)^{12}}{\left(\frac{1}{4}\right)^{12}+\left(\frac{1}{4}\right)^{13}}$$

Calculate \frac{1}{4} to the power of 12 and get \frac{1}{16777216}.

$$\frac{\frac{1}{4194304}-\frac{1}{16777216}}{\left(\frac{1}{4}\right)^{12}+\left(\frac{1}{4}\right)^{13}}$$

Least common multiple of 4194304 and 16777216 is 16777216. Convert \frac{1}{4194304} and \frac{1}{16777216} to fractions with denominator 16777216.

$$\frac{\frac{4}{16777216}-\frac{1}{16777216}}{\left(\frac{1}{4}\right)^{12}+\left(\frac{1}{4}\right)^{13}}$$

Since \frac{4}{16777216} and \frac{1}{16777216} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-1}{16777216}}{\left(\frac{1}{4}\right)^{12}+\left(\frac{1}{4}\right)^{13}}$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{3}{16777216}}{\left(\frac{1}{4}\right)^{12}+\left(\frac{1}{4}\right)^{13}}$$

Calculate \frac{1}{4} to the power of 12 and get \frac{1}{16777216}.

$$\frac{\frac{3}{16777216}}{\frac{1}{16777216}+\left(\frac{1}{4}\right)^{13}}$$

Calculate \frac{1}{4} to the power of 13 and get \frac{1}{67108864}.

$$\frac{\frac{3}{16777216}}{\frac{1}{16777216}+\frac{1}{67108864}}$$

Least common multiple of 16777216 and 67108864 is 67108864. Convert \frac{1}{16777216} and \frac{1}{67108864} to fractions with denominator 67108864.

$$\frac{\frac{3}{16777216}}{\frac{4}{67108864}+\frac{1}{67108864}}$$

Since \frac{4}{67108864} and \frac{1}{67108864} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{16777216}}{\frac{4+1}{67108864}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{3}{16777216}}{\frac{5}{67108864}}$$

Divide \frac{3}{16777216} by \frac{5}{67108864} by multiplying \frac{3}{16777216} by the reciprocal of \frac{5}{67108864}.

$$\frac{3}{16777216}\times \frac{67108864}{5}$$

Multiply \frac{3}{16777216} times \frac{67108864}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 67108864}{16777216\times 5}$$

Do the multiplications in the fraction \frac{3\times 67108864}{16777216\times 5}.

$$\frac{201326592}{83886080}$$

Reduce the fraction \frac{201326592}{83886080} to lowest terms by extracting and canceling out 16777216.

$$\frac{12}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 3}{5} = 2\frac{2}{5} = 2.4$$