Solve (1-1/2^2)(1-1/3^2)(1-1/4^2)

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

Evaluate

$$\frac{5}{8}=0.625$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\left(1-\frac{1}{4}\right)\left(1-\frac{1}{3^{2}}\right)\left(1-\frac{1}{4^{2}}\right)$$

Convert 1 to fraction \frac{4}{4}.

$$\left(\frac{4}{4}-\frac{1}{4}\right)\left(1-\frac{1}{3^{2}}\right)\left(1-\frac{1}{4^{2}}\right)$$

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

$$\frac{4-1}{4}\left(1-\frac{1}{3^{2}}\right)\left(1-\frac{1}{4^{2}}\right)$$

Subtract 1 from 4 to get 3.

$$\frac{3}{4}\left(1-\frac{1}{3^{2}}\right)\left(1-\frac{1}{4^{2}}\right)$$

Calculate 3 to the power of 2 and get 9.

$$\frac{3}{4}\left(1-\frac{1}{9}\right)\left(1-\frac{1}{4^{2}}\right)$$

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

$$\frac{3}{4}\left(\frac{9}{9}-\frac{1}{9}\right)\left(1-\frac{1}{4^{2}}\right)$$

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

$$\frac{3}{4}\times \frac{9-1}{9}\left(1-\frac{1}{4^{2}}\right)$$

Subtract 1 from 9 to get 8.

$$\frac{3}{4}\times \frac{8}{9}\left(1-\frac{1}{4^{2}}\right)$$

Multiply \frac{3}{4} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 8}{4\times 9}\left(1-\frac{1}{4^{2}}\right)$$

Do the multiplications in the fraction \frac{3\times 8}{4\times 9}.

$$\frac{24}{36}\left(1-\frac{1}{4^{2}}\right)$$

Reduce the fraction \frac{24}{36} to lowest terms by extracting and canceling out 12.

$$\frac{2}{3}\left(1-\frac{1}{4^{2}}\right)$$

Calculate 4 to the power of 2 and get 16.

$$\frac{2}{3}\left(1-\frac{1}{16}\right)$$

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

$$\frac{2}{3}\left(\frac{16}{16}-\frac{1}{16}\right)$$

Since \frac{16}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}\times \frac{16-1}{16}$$

Subtract 1 from 16 to get 15.

$$\frac{2}{3}\times \frac{15}{16}$$

Multiply \frac{2}{3} times \frac{15}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 15}{3\times 16}$$

Do the multiplications in the fraction \frac{2\times 15}{3\times 16}.

$$\frac{30}{48}$$

Reduce the fraction \frac{30}{48} to lowest terms by extracting and canceling out 6.

$$\frac{5}{8}$$

Factor

$$\frac{5}{2 ^ {3}} = 0.625$$