Solve (4/3)^2*(4/3)^4-2quad(4/3)^3

$$( \frac { 4 } { 3 } ) ^ { 2 } \times ( \frac { 4 } { 3 } ) ^ { 4 - 2 } \quad ( \frac { 4 } { 3 } ) ^ { 3 }$$

Evaluate

$$\frac{16384}{2187}\approx 7.491540924$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\left(\frac{4}{3}\right)^{5}\times \left(\frac{4}{3}\right)^{4-2}$$

Calculate \frac{4}{3} to the power of 5 and get \frac{1024}{243}.

$$\frac{1024}{243}\times \left(\frac{4}{3}\right)^{4-2}$$

Subtract 2 from 4 to get 2.

$$\frac{1024}{243}\times \left(\frac{4}{3}\right)^{2}$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{1024}{243}\times \frac{16}{9}$$

Multiply \frac{1024}{243} and \frac{16}{9} to get \frac{16384}{2187}.

$$\frac{16384}{2187}$$

Factor

$$\frac{2 ^ {14}}{3 ^ {7}} = 7\frac{1075}{2187} = 7.491540923639689$$