Solve [2^9:(2^3)^2]*(-2)^4

$$[ 2 ^ { 9 } : ( 2 ^ { 3 } ) ^ { 2 } ] \cdot ( - 2 ) ^ { 4 }$$

Evaluate

$$128$$

Solution Steps

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

$$\frac{2^{9}}{2^{6}}\left(-2\right)^{4}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 9 to get 3.

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

Calculate 2 to the power of 3 and get 8.

$$8\left(-2\right)^{4}$$

Calculate -2 to the power of 4 and get 16.

$$8\times 16$$

Multiply 8 and 16 to get 128.

$$128$$

Factor

$$2^{7}$$