Solve (7/8)^3div(8/7)^-3-(1/3-1)^0+3^-1

$$( \frac { 7 } { 8 } ) ^ { 3 } \div ( \frac { 8 } { 7 } ) ^ { - 3 } - ( \frac { 1 } { 3 } - 1 ) ^ { 0 } + 3 ^ { - 1 }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Calculate \frac{7}{8} to the power of 3 and get \frac{343}{512}.

$$\frac{\frac{343}{512}}{\left(\frac{8}{7}\right)^{-3}}-\left(\frac{1}{3}-1\right)^{0}+3^{-1}$$

Calculate \frac{8}{7} to the power of -3 and get \frac{343}{512}.

$$\frac{\frac{343}{512}}{\frac{343}{512}}-\left(\frac{1}{3}-1\right)^{0}+3^{-1}$$

Divide \frac{343}{512} by \frac{343}{512} to get 1.

$$1-\left(\frac{1}{3}-1\right)^{0}+3^{-1}$$

Subtract 1 from \frac{1}{3} to get -\frac{2}{3}.

$$1-\left(-\frac{2}{3}\right)^{0}+3^{-1}$$

Calculate -\frac{2}{3} to the power of 0 and get 1.

$$1-1+3^{-1}$$

Subtract 1 from 1 to get 0.

$$0+3^{-1}$$

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

$$0+\frac{1}{3}$$

Add 0 and \frac{1}{3} to get \frac{1}{3}.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$