Solve frac{(8)^frac{2{3}}-(81)^frac{3{4}}}{(27)^frac{2{3}}+(64)^frac{1{6}}}=

$$\frac { ( 8 ) ^ { \frac { 2 } { 3 } } - ( 81 ) ^ { \frac { 3 } { 4 } } } { ( 27 ) ^ { \frac { 2 } { 3 } } + ( 64 ) ^ { \frac { 1 } { 6 } } } =$$

Evaluate

$$-\frac{23}{11}\approx -2.090909091$$

Solution Steps

Calculate 8 to the power of \frac{2}{3} and get 4.

$$\frac{4-81^{\frac{3}{4}}}{27^{\frac{2}{3}}+64^{\frac{1}{6}}}$$

Calculate 81 to the power of \frac{3}{4} and get 27.

$$\frac{4-27}{27^{\frac{2}{3}}+64^{\frac{1}{6}}}$$

Subtract 27 from 4 to get -23.

$$\frac{-23}{27^{\frac{2}{3}}+64^{\frac{1}{6}}}$$

Calculate 27 to the power of \frac{2}{3} and get 9.

$$\frac{-23}{9+64^{\frac{1}{6}}}$$

Calculate 64 to the power of \frac{1}{6} and get 2.

$$\frac{-23}{9+2}$$

Add 9 and 2 to get 11.

$$\frac{-23}{11}$$

Fraction \frac{-23}{11} can be rewritten as -\frac{23}{11} by extracting the negative sign.

$$-\frac{23}{11}$$

Factor

$$-\frac{23}{11} = -2\frac{1}{11} = -2.090909090909091$$