Solve (52/3)^18/(52/3)^16

$$( 5 \frac { 2 } { 3 } ) ^ { 18 } / ( 5 \frac { 2 } { 3 } ) ^ { 16 }$$

Evaluate

$$\frac{289}{9}\approx 32.111111111$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 16 from 18 to get 2.

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

Multiply 5 and 3 to get 15.

$$\left(\frac{15+2}{3}\right)^{2}$$

Add 15 and 2 to get 17.

$$\left(\frac{17}{3}\right)^{2}$$

Calculate \frac{17}{3} to the power of 2 and get \frac{289}{9}.

$$\frac{289}{9}$$

Factor

$$\frac{17 ^ {2}}{3 ^ {2}} = 32\frac{1}{9} = 32.111111111111114$$