Solve 1-3*(1/4)^2+(1/4)^3/frac{1{4}*(1-1/y)}

$$\frac { 1 - 3 \cdot ( \frac { 1 } { 4 } ) ^ { 2 } + ( \frac { 1 } { 4 } ) ^ { 3 } } { \frac { 1 } { 4 } \cdot ( 1 - \frac { 1 } { y } ) }$$

Evaluate

$$\frac{53y}{16\left(y-1\right)}$$

Short Solution Steps

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{1-3\times \frac{1}{16}+\left(\frac{1}{4}\right)^{3}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Multiply 3 and \frac{1}{16} to get \frac{3}{16}.

$$\frac{1-\frac{3}{16}+\left(\frac{1}{4}\right)^{3}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Convert 1 to fraction \frac{16}{16}.

$$\frac{\frac{16}{16}-\frac{3}{16}+\left(\frac{1}{4}\right)^{3}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Since \frac{16}{16} and \frac{3}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16-3}{16}+\left(\frac{1}{4}\right)^{3}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Subtract 3 from 16 to get 13.

$$\frac{\frac{13}{16}+\left(\frac{1}{4}\right)^{3}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Calculate \frac{1}{4} to the power of 3 and get \frac{1}{64}.

$$\frac{\frac{13}{16}+\frac{1}{64}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Least common multiple of 16 and 64 is 64. Convert \frac{13}{16} and \frac{1}{64} to fractions with denominator 64.

$$\frac{\frac{52}{64}+\frac{1}{64}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Since \frac{52}{64} and \frac{1}{64} have the same denominator, add them by adding their numerators.

$$\frac{\frac{52+1}{64}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Add 52 and 1 to get 53.

$$\frac{\frac{53}{64}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y}{y}.

$$\frac{\frac{53}{64}}{\frac{1}{4}\left(\frac{y}{y}-\frac{1}{y}\right)}$$

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

$$\frac{\frac{53}{64}}{\frac{1}{4}\times \frac{y-1}{y}}$$

Multiply \frac{1}{4} times \frac{y-1}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{53}{64}}{\frac{y-1}{4y}}$$

Divide \frac{53}{64} by \frac{y-1}{4y} by multiplying \frac{53}{64} by the reciprocal of \frac{y-1}{4y}.

$$\frac{53\times 4y}{64\left(y-1\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{53y}{16\left(y-1\right)}$$

Use the distributive property to multiply 16 by y-1.

$$\frac{53y}{16y-16}$$

Expand

$$\frac{53y}{16\left(y-1\right)}$$

Short Solution Steps

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{1-3\times \frac{1}{16}+\left(\frac{1}{4}\right)^{3}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Multiply 3 and \frac{1}{16} to get \frac{3}{16}.

$$\frac{1-\frac{3}{16}+\left(\frac{1}{4}\right)^{3}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Convert 1 to fraction \frac{16}{16}.

$$\frac{\frac{16}{16}-\frac{3}{16}+\left(\frac{1}{4}\right)^{3}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Since \frac{16}{16} and \frac{3}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16-3}{16}+\left(\frac{1}{4}\right)^{3}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Subtract 3 from 16 to get 13.

$$\frac{\frac{13}{16}+\left(\frac{1}{4}\right)^{3}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Calculate \frac{1}{4} to the power of 3 and get \frac{1}{64}.

$$\frac{\frac{13}{16}+\frac{1}{64}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Least common multiple of 16 and 64 is 64. Convert \frac{13}{16} and \frac{1}{64} to fractions with denominator 64.

$$\frac{\frac{52}{64}+\frac{1}{64}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Since \frac{52}{64} and \frac{1}{64} have the same denominator, add them by adding their numerators.

$$\frac{\frac{52+1}{64}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

Add 52 and 1 to get 53.

$$\frac{\frac{53}{64}}{\frac{1}{4}\left(1-\frac{1}{y}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y}{y}.

$$\frac{\frac{53}{64}}{\frac{1}{4}\left(\frac{y}{y}-\frac{1}{y}\right)}$$

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

$$\frac{\frac{53}{64}}{\frac{1}{4}\times \frac{y-1}{y}}$$

Multiply \frac{1}{4} times \frac{y-1}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{53}{64}}{\frac{y-1}{4y}}$$

Divide \frac{53}{64} by \frac{y-1}{4y} by multiplying \frac{53}{64} by the reciprocal of \frac{y-1}{4y}.

$$\frac{53\times 4y}{64\left(y-1\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{53y}{16\left(y-1\right)}$$

Use the distributive property to multiply 16 by y-1.

$$\frac{53y}{16y-16}$$