Solve {left|{left(9/16right)}^frac{-2{3}}right|}^frac{3{4}}

$${ \left| { \left( \frac{ 9 }{ 16 } \right) }^{ \frac{ -2 }{ 3 } } \right| }^{ \frac{ 3 }{ 4 } }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{9}{16} is \frac{9}{16}.

$$\left(\left(\frac{9}{16}\right)^{\frac{-2}{3}}\right)^{\frac{3}{4}}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\left(\left(\frac{9}{16}\right)^{-\frac{2}{3}}\right)^{\frac{3}{4}}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$