Solve frac{2^{3}*2^{7}*2^{-3}*2^{5}}{2^4*2^6*2^-2*2^9}

$$\frac { 2 ^ { 3 } \cdot 2 ^ { 7 } \cdot 2 ^ { - 3 } \cdot 2 ^ { 5 } } { 2 ^ { 4 } \cdot 2 ^ { 6 } \cdot 2 ^ { - 2 } \cdot 2 ^ { 9 } }$$

Evaluate

$$\frac{1}{32}=0.03125$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$\frac{2^{10}\times 2^{-3}\times 2^{5}}{2^{4}\times 2^{6}\times 2^{-2}\times 2^{9}}$$

To multiply powers of the same base, add their exponents. Add 10 and -3 to get 7.

$$\frac{2^{7}\times 2^{5}}{2^{4}\times 2^{6}\times 2^{-2}\times 2^{9}}$$

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

$$\frac{2^{12}}{2^{4}\times 2^{6}\times 2^{-2}\times 2^{9}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{2^{12}}{2^{10}\times 2^{-2}\times 2^{9}}$$

To multiply powers of the same base, add their exponents. Add 10 and -2 to get 8.

$$\frac{2^{12}}{2^{8}\times 2^{9}}$$

To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.

$$\frac{2^{12}}{2^{17}}$$

Rewrite 2^{17} as 2^{12}\times 2^{5}. Cancel out 2^{12} in both numerator and denominator.

$$\frac{1}{2^{5}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{1}{32}$$

Factor

$$\frac{1}{2 ^ {5}} = 0.03125$$