Solve (2^5*2^4)/(2*2^7)^4

$$\frac { ( 2 ^ { 5 } \cdot 2 ^ { 4 } ) } { ( 2 \cdot 2 ^ { 7 } ) ^ { 4 } }$$

Evaluate

$$\frac{1}{8388608}\approx 0.000000119$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{2^{9}}{\left(2\times 2^{7}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$\frac{2^{9}}{\left(2^{8}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 4 to get 32.

$$\frac{2^{9}}{2^{32}}$$

Rewrite 2^{32} as 2^{9}\times 2^{23}. Cancel out 2^{9} in both numerator and denominator.

$$\frac{1}{2^{23}}$$

Calculate 2 to the power of 23 and get 8388608.

$$\frac{1}{8388608}$$

Factor

$$\frac{1}{2 ^ {23}} = 1.1920928955078125 \times 10^{-7}$$