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

$$\frac { 2 ^ { 3 } \cdot 2 ^ { 2 } } { ( 2 ^ { 2 } ) ^ { - 2 } }$$

Evaluate

$$512$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

$$\frac{2^{5}}{2^{-4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -4 from 5 to get 9.

$$2^{9}$$

Calculate 2 to the power of 9 and get 512.

$$512$$

Factor

$$2^{9}$$