Solve 4/3(9)^1frac{1{2}}-2*9^frac{1{2}}-(4/3*(4)^frac{1{2}}-2*(4)^2)

$$\frac { 4 } { 3 } ( 9 ) ^ { 1 \frac { 1 } { 2 } } - 2 \cdot 9 ^ { \frac { 1 } { 2 } } - ( \frac { 4 } { 3 } \cdot ( 4 ) ^ { \frac { 1 } { 2 } } - 2 \cdot ( 4 ) ^ { 2 } )$$

Evaluate

$$\frac{178}{3}\approx 59.333333333$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{4}{3}\times 9^{\frac{2+1}{2}}-2\times 9^{\frac{1}{2}}-\left(\frac{4}{3}\times 4^{\frac{1}{2}}-2\times 4^{2}\right)$$

Add 2 and 1 to get 3.

$$\frac{4}{3}\times 9^{\frac{3}{2}}-2\times 9^{\frac{1}{2}}-\left(\frac{4}{3}\times 4^{\frac{1}{2}}-2\times 4^{2}\right)$$

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

$$\frac{4}{3}\times 27-2\times 9^{\frac{1}{2}}-\left(\frac{4}{3}\times 4^{\frac{1}{2}}-2\times 4^{2}\right)$$

Multiply \frac{4}{3} and 27 to get 36.

$$36-2\times 9^{\frac{1}{2}}-\left(\frac{4}{3}\times 4^{\frac{1}{2}}-2\times 4^{2}\right)$$

Calculate 9 to the power of \frac{1}{2} and get 3.

$$36-2\times 3-\left(\frac{4}{3}\times 4^{\frac{1}{2}}-2\times 4^{2}\right)$$

Multiply 2 and 3 to get 6.

$$36-6-\left(\frac{4}{3}\times 4^{\frac{1}{2}}-2\times 4^{2}\right)$$

Subtract 6 from 36 to get 30.

$$30-\left(\frac{4}{3}\times 4^{\frac{1}{2}}-2\times 4^{2}\right)$$

Calculate 4 to the power of \frac{1}{2} and get 2.

$$30-\left(\frac{4}{3}\times 2-2\times 4^{2}\right)$$

Multiply \frac{4}{3} and 2 to get \frac{8}{3}.

$$30-\left(\frac{8}{3}-2\times 4^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$30-\left(\frac{8}{3}-2\times 16\right)$$

Multiply 2 and 16 to get 32.

$$30-\left(\frac{8}{3}-32\right)$$

Subtract 32 from \frac{8}{3} to get -\frac{88}{3}.

$$30-\left(-\frac{88}{3}\right)$$

The opposite of -\frac{88}{3} is \frac{88}{3}.

$$30+\frac{88}{3}$$

Add 30 and \frac{88}{3} to get \frac{178}{3}.

$$\frac{178}{3}$$

Factor

$$\frac{2 \cdot 89}{3} = 59\frac{1}{3} = 59.333333333333336$$