Solve A_2^2*4*5*(2/3)^4(1/3)^3+4*5*(2/3)^4(1/3)^3=

$$A _ { 2 } ^ { 2 } \times 4 \times 5 \times ( \frac { 2 } { 3 } ) ^ { 4 } ( \frac { 1 } { 3 } ) ^ { 3 } + 4 \times 5 \times ( \frac { 2 } { 3 } ) ^ { 4 } ( \frac { 1 } { 3 } ) ^ { 3 } =$$

Evaluate

$$\frac{320\left(A_{2}^{2}+1\right)}{2187}$$

Solution Steps

Multiply 4 and 5 to get 20.

$$A_{2}^{2}\times 20\times \left(\frac{2}{3}\right)^{4}\times \left(\frac{1}{3}\right)^{3}+4\times 5\times \left(\frac{2}{3}\right)^{4}\times \left(\frac{1}{3}\right)^{3}$$

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$A_{2}^{2}\times 20\times \frac{16}{81}\times \left(\frac{1}{3}\right)^{3}+4\times 5\times \left(\frac{2}{3}\right)^{4}\times \left(\frac{1}{3}\right)^{3}$$

Multiply 20 and \frac{16}{81} to get \frac{320}{81}.

$$A_{2}^{2}\times \frac{320}{81}\times \left(\frac{1}{3}\right)^{3}+4\times 5\times \left(\frac{2}{3}\right)^{4}\times \left(\frac{1}{3}\right)^{3}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$A_{2}^{2}\times \frac{320}{81}\times \frac{1}{27}+4\times 5\times \left(\frac{2}{3}\right)^{4}\times \left(\frac{1}{3}\right)^{3}$$

Multiply \frac{320}{81} and \frac{1}{27} to get \frac{320}{2187}.

$$A_{2}^{2}\times \frac{320}{2187}+4\times 5\times \left(\frac{2}{3}\right)^{4}\times \left(\frac{1}{3}\right)^{3}$$

Multiply 4 and 5 to get 20.

$$A_{2}^{2}\times \frac{320}{2187}+20\times \left(\frac{2}{3}\right)^{4}\times \left(\frac{1}{3}\right)^{3}$$

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$A_{2}^{2}\times \frac{320}{2187}+20\times \frac{16}{81}\times \left(\frac{1}{3}\right)^{3}$$

Multiply 20 and \frac{16}{81} to get \frac{320}{81}.

$$A_{2}^{2}\times \frac{320}{2187}+\frac{320}{81}\times \left(\frac{1}{3}\right)^{3}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$A_{2}^{2}\times \frac{320}{2187}+\frac{320}{81}\times \frac{1}{27}$$

Multiply \frac{320}{81} and \frac{1}{27} to get \frac{320}{2187}.

$$A_{2}^{2}\times \frac{320}{2187}+\frac{320}{2187}$$

Factor

$$\frac{320\left(A_{2}^{2}+1\right)}{2187}$$

Solution Steps

Factor out \frac{320}{2187}. Polynomial A_{2}^{2}+1 is not factored since it does not have any rational roots.

$$\frac{320\left(A_{2}^{2}+1\right)}{2187}$$