Solve frac{2^{5}*2^{7}*(2^2)^4}{2^24*2^-3}

$$\frac { 2 ^ { 5 } \times 2 ^ { 7 } \times ( 2 ^ { 2 } ) ^ { 4 } } { 2 ^ { 24 } \cdot 2 ^ { - 3 } }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{2^{5}\times 2^{7}\times 2^{8}}{2^{24}\times 2^{-3}}$$

To multiply powers of the same base, add their exponents. Add 5 and 7 to get 12.

$$\frac{2^{12}\times 2^{8}}{2^{24}\times 2^{-3}}$$

To multiply powers of the same base, add their exponents. Add 12 and 8 to get 20.

$$\frac{2^{20}}{2^{24}\times 2^{-3}}$$

To multiply powers of the same base, add their exponents. Add 24 and -3 to get 21.

$$\frac{2^{20}}{2^{21}}$$

Rewrite 2^{21} as 2\times 2^{20}. Cancel out 2^{20} in both numerator and denominator.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$