Solve 2^-11*left(2^3right)^-4*(2^5)/{2^-4{2}^7}

$$\frac{ { 2 }^{ -11 } \times { \left( { 2 }^{ 3 } \right) }^{ -4 } \times ( { 2 }^{ 5 } ) }{ { 2 }^{ -4 } { 2 }^{ 7 } }$$

Evaluate

$$\frac{1}{2097152}\approx 0.000000477$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and -4 to get -12.

$$\frac{2^{-11}\times 2^{-12}\times 2^{5}}{2^{-4}\times 2^{7}}$$

To multiply powers of the same base, add their exponents. Add -11 and -12 to get -23.

$$\frac{2^{-23}\times 2^{5}}{2^{-4}\times 2^{7}}$$

To multiply powers of the same base, add their exponents. Add -23 and 5 to get -18.

$$\frac{2^{-18}}{2^{-4}\times 2^{7}}$$

To multiply powers of the same base, add their exponents. Add -4 and 7 to get 3.

$$\frac{2^{-18}}{2^{3}}$$

Rewrite 2^{3} as 2^{-18}\times 2^{21}. Cancel out 2^{-18} in both numerator and denominator.

$$\frac{1}{2^{21}}$$

Calculate 2 to the power of 21 and get 2097152.

$$\frac{1}{2097152}$$

Factor

$$\frac{1}{2 ^ {21}} = 4.76837158203125 \times 10^{-7}$$