Solve 4^{-frac{1/6}*9^{3/8}*6^-3}{4^frac{5{6}}*9^-frac{5{8}}*6^-3}

$$\frac { 4 ^ { - \frac { 1 } { 6 } } \cdot 9 ^ { \frac { 3 } { 8 } } \cdot 6 ^ { - 3 } } { 4 ^ { \frac { 5 } { 6 } } \cdot 9 ^ { - \frac { 5 } { 8 } } \cdot 6 ^ { - 3 } }$$

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

Cancel out 6^{-3} in both numerator and denominator.

$$\frac{4^{-\frac{1}{6}}\times 9^{\frac{3}{8}}}{4^{\frac{5}{6}}\times 9^{-\frac{5}{8}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{4^{-\frac{1}{6}}\times 9^{1}}{4^{\frac{5}{6}}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{9^{1}}{4^{1}}$$

Calculate 9 to the power of 1 and get 9.

$$\frac{9}{4^{1}}$$

Calculate 4 to the power of 1 and get 4.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$