Solve a1-1/8^6/1-frac{1{3^2}}=2457

$$a \frac { 1 - \frac { 1 } { 8 ^ { 6 } } } { 1 - \frac { 1 } { 3 ^ { 2 } } } = 2457$$

Solve for a

$$a = \frac{27262976}{12483} = 2184\frac{104}{12483} \approx 2184.008331331$$

Steps for Solving Linear Equation

Calculate 8 to the power of 6 and get 262144.

$$a\times \frac{1-\frac{1}{262144}}{1-\frac{1}{3^{2}}}=2457$$

Convert 1 to fraction \frac{262144}{262144}.

$$a\times \frac{\frac{262144}{262144}-\frac{1}{262144}}{1-\frac{1}{3^{2}}}=2457$$

Since \frac{262144}{262144} and \frac{1}{262144} have the same denominator, subtract them by subtracting their numerators.

$$a\times \frac{\frac{262144-1}{262144}}{1-\frac{1}{3^{2}}}=2457$$

Subtract 1 from 262144 to get 262143.

$$a\times \frac{\frac{262143}{262144}}{1-\frac{1}{3^{2}}}=2457$$

Calculate 3 to the power of 2 and get 9.

$$a\times \frac{\frac{262143}{262144}}{1-\frac{1}{9}}=2457$$

Convert 1 to fraction \frac{9}{9}.

$$a\times \frac{\frac{262143}{262144}}{\frac{9}{9}-\frac{1}{9}}=2457$$

Since \frac{9}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$a\times \frac{\frac{262143}{262144}}{\frac{9-1}{9}}=2457$$

Subtract 1 from 9 to get 8.

$$a\times \frac{\frac{262143}{262144}}{\frac{8}{9}}=2457$$

Divide \frac{262143}{262144} by \frac{8}{9} by multiplying \frac{262143}{262144} by the reciprocal of \frac{8}{9}.

$$a\times \frac{262143}{262144}\times \frac{9}{8}=2457$$

Multiply \frac{262143}{262144} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$a\times \frac{262143\times 9}{262144\times 8}=2457$$

Do the multiplications in the fraction \frac{262143\times 9}{262144\times 8}.

$$a\times \frac{2359287}{2097152}=2457$$

Multiply both sides by \frac{2097152}{2359287}, the reciprocal of \frac{2359287}{2097152}.

$$a=2457\times \frac{2097152}{2359287}$$

Express 2457\times \frac{2097152}{2359287} as a single fraction.

$$a=\frac{2457\times 2097152}{2359287}$$

Multiply 2457 and 2097152 to get 5152702464.

$$a=\frac{5152702464}{2359287}$$

Reduce the fraction \frac{5152702464}{2359287} to lowest terms by extracting and canceling out 189.

$$a=\frac{27262976}{12483}$$