Solve [(4/3)^2]^3:(4/3)^4

$$[ ( \frac { 4 } { 3 } ) ^ { 2 } ] ^ { 3 } : ( \frac { 4 } { 3 } ) ^ { 4 }$$

Evaluate

$$\frac{16}{9}\approx 1.777777778$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(\frac{4}{3}\right)^{6}}{\left(\frac{4}{3}\right)^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

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

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

$$\frac{16}{9}$$

Factor

$$\frac{2 ^ {4}}{3 ^ {2}} = 1\frac{7}{9} = 1.7777777777777777$$