Solve {left(-1/3+1/2right)}^-2+sqrt[4]{{left(9/4right)}^-2}{left(7/6-1right)}^-2

$${ \left(- \frac{ 1 }{ 3 } + \frac{ 1 }{ 2 } \right) }^{ -2 } + \sqrt[ 4 ]{ { \left( \frac{ 9 }{ 4 } \right) }^{ -2 } } { \left( \frac{ 7 }{ 6 } -1 \right) }^{ -2 }$$

Evaluate

$$60$$

Solution Steps

Add -\frac{1}{3} and \frac{1}{2} to get \frac{1}{6}.

$$\left(\frac{1}{6}\right)^{-2}+\sqrt[4]{\left(\frac{9}{4}\right)^{-2}}\left(\frac{7}{6}-1\right)^{-2}$$

Calculate \frac{1}{6} to the power of -2 and get 36.

$$36+\sqrt[4]{\left(\frac{9}{4}\right)^{-2}}\left(\frac{7}{6}-1\right)^{-2}$$

Calculate \frac{9}{4} to the power of -2 and get \frac{16}{81}.

$$36+\sqrt[4]{\frac{16}{81}}\left(\frac{7}{6}-1\right)^{-2}$$

Calculate \sqrt[4]{\frac{16}{81}} and get \frac{2}{3}.

$$36+\frac{2}{3}\left(\frac{7}{6}-1\right)^{-2}$$

Subtract 1 from \frac{7}{6} to get \frac{1}{6}.

$$36+\frac{2}{3}\times \left(\frac{1}{6}\right)^{-2}$$

Calculate \frac{1}{6} to the power of -2 and get 36.

$$36+\frac{2}{3}\times 36$$

Multiply \frac{2}{3} and 36 to get 24.

$$36+24$$

Add 36 and 24 to get 60.

$$60$$

Factor

$$2^{2}\times 3\times 5$$