Solve (7/6):(7/6):(7/6)*(7/6)^3:(frac{7}{6})^4-(frac{1}{2})^6:(frac{1}{2})^5*(frac{1}{2})

$$( \frac { 7 } { 6 } ) : ( \frac { 7 } { 6 } ) : ( \frac { 7 } { 6 } ) \cdot ( \frac { 7 } { 6 } ) ^ { 3 } : ( \frac { 7 } { 6 } ) ^ { 4 } - ( \frac { 1 } { 2 } ) ^ { 6 } : ( \frac { 1 } { 2 } ) ^ { 5 } \cdot ( \frac { 1 } { 2 } )$$

Evaluate

$$\frac{95}{196}\approx 0.484693878$$

Solution Steps

Divide \frac{7}{6} by \frac{7}{6} to get 1.

$$\frac{\frac{1}{\frac{7}{6}}\times \left(\frac{7}{6}\right)^{3}}{\left(\frac{7}{6}\right)^{4}}-\frac{\left(\frac{1}{2}\right)^{6}}{\left(\frac{1}{2}\right)^{5}}\times \frac{1}{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 6 to get 1.

$$\frac{\frac{1}{\frac{7}{6}}\times \left(\frac{7}{6}\right)^{3}}{\left(\frac{7}{6}\right)^{4}}-\left(\frac{1}{2}\right)^{1}\times \frac{1}{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 1 to get 2.

$$\frac{\frac{1}{\frac{7}{6}}\times \left(\frac{7}{6}\right)^{3}}{\left(\frac{7}{6}\right)^{4}}-\left(\frac{1}{2}\right)^{2}$$

Divide 1 by \frac{7}{6} by multiplying 1 by the reciprocal of \frac{7}{6}.

$$\frac{1\times \frac{6}{7}\times \left(\frac{7}{6}\right)^{3}}{\left(\frac{7}{6}\right)^{4}}-\left(\frac{1}{2}\right)^{2}$$

Multiply 1 and \frac{6}{7} to get \frac{6}{7}.

$$\frac{\frac{6}{7}\times \left(\frac{7}{6}\right)^{3}}{\left(\frac{7}{6}\right)^{4}}-\left(\frac{1}{2}\right)^{2}$$

Calculate \frac{7}{6} to the power of 3 and get \frac{343}{216}.

$$\frac{\frac{6}{7}\times \frac{343}{216}}{\left(\frac{7}{6}\right)^{4}}-\left(\frac{1}{2}\right)^{2}$$

Multiply \frac{6}{7} times \frac{343}{216} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{6\times 343}{7\times 216}}{\left(\frac{7}{6}\right)^{4}}-\left(\frac{1}{2}\right)^{2}$$

Do the multiplications in the fraction \frac{6\times 343}{7\times 216}.

$$\frac{\frac{2058}{1512}}{\left(\frac{7}{6}\right)^{4}}-\left(\frac{1}{2}\right)^{2}$$

Reduce the fraction \frac{2058}{1512} to lowest terms by extracting and canceling out 42.

$$\frac{\frac{49}{36}}{\left(\frac{7}{6}\right)^{4}}-\left(\frac{1}{2}\right)^{2}$$

Calculate \frac{7}{6} to the power of 4 and get \frac{2401}{1296}.

$$\frac{\frac{49}{36}}{\frac{2401}{1296}}-\left(\frac{1}{2}\right)^{2}$$

Divide \frac{49}{36} by \frac{2401}{1296} by multiplying \frac{49}{36} by the reciprocal of \frac{2401}{1296}.

$$\frac{49}{36}\times \frac{1296}{2401}-\left(\frac{1}{2}\right)^{2}$$

Multiply \frac{49}{36} times \frac{1296}{2401} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 1296}{36\times 2401}-\left(\frac{1}{2}\right)^{2}$$

Do the multiplications in the fraction \frac{49\times 1296}{36\times 2401}.

$$\frac{63504}{86436}-\left(\frac{1}{2}\right)^{2}$$

Reduce the fraction \frac{63504}{86436} to lowest terms by extracting and canceling out 1764.

$$\frac{36}{49}-\left(\frac{1}{2}\right)^{2}$$

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

$$\frac{36}{49}-\frac{1}{4}$$

Least common multiple of 49 and 4 is 196. Convert \frac{36}{49} and \frac{1}{4} to fractions with denominator 196.

$$\frac{144}{196}-\frac{49}{196}$$

Since \frac{144}{196} and \frac{49}{196} have the same denominator, subtract them by subtracting their numerators.

$$\frac{144-49}{196}$$

Subtract 49 from 144 to get 95.

$$\frac{95}{196}$$

Factor

$$\frac{5 \cdot 19}{2 ^ {2} \cdot 7 ^ {2}} = 0.4846938775510204$$