Solve (2^5*2^-3)div(2^9)^-2

$$( 2 ^ { 5 } \cdot 2 ^ { - 3 } ) \div ( 2 ^ { 9 } ) ^ { - 2 }$$

Evaluate

$$1048576$$

Solution Steps

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

$$\frac{2^{2}}{\left(2^{9}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and -2 to get -18.

$$\frac{2^{2}}{2^{-18}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -18 from 2 to get 20.

$$2^{20}$$

Calculate 2 to the power of 20 and get 1048576.

$$1048576$$

Factor

$$2^{20}$$