Solve (2^2)^7/(3^5)^2

$$\frac { ( 2 ^ { 2 } ) ^ { 7 } } { ( 3 ^ { 5 } ) ^ { 2 } }$$

Evaluate

$$\frac{16384}{59049}\approx 0.277464479$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 7 to get 14.

$$\frac{2^{14}}{\left(3^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{2^{14}}{3^{10}}$$

Calculate 2 to the power of 14 and get 16384.

$$\frac{16384}{3^{10}}$$

Calculate 3 to the power of 10 and get 59049.

$$\frac{16384}{59049}$$

Factor

$$\frac{2 ^ {14}}{3 ^ {10}} = 0.2774644786533218$$