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

$$( \frac { ( 2 ^ { 2 } ) ^ { - 3 } } { 2 ^ { - 3 } } ) ^ { 3 } \cdot ( 2 ^ { - 5 } \cdot 2 ^ { 4 } ) ^ { 3 } =$$

Evaluate

$$\frac{1}{4096}=0.000244141$$

Solution Steps

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

$$\left(\frac{2^{-6}}{2^{-3}}\right)^{3}\times \left(2^{-5}\times 2^{4}\right)^{3}$$

Rewrite 2^{-3} as 2^{-6}\times 2^{3}. Cancel out 2^{-6} in both numerator and denominator.

$$\left(\frac{1}{2^{3}}\right)^{3}\times \left(2^{-5}\times 2^{4}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add -5 and 4 to get -1.

$$\left(\frac{1}{2^{3}}\right)^{3}\times \left(2^{-1}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

$$\left(\frac{1}{2^{3}}\right)^{3}\times 2^{-3}$$

Calculate 2 to the power of 3 and get 8.

$$\left(\frac{1}{8}\right)^{3}\times 2^{-3}$$

Calculate \frac{1}{8} to the power of 3 and get \frac{1}{512}.

$$\frac{1}{512}\times 2^{-3}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{1}{512}\times \frac{1}{8}$$

Multiply \frac{1}{512} and \frac{1}{8} to get \frac{1}{4096}.

$$\frac{1}{4096}$$

Factor

$$\frac{1}{2 ^ {12}} = 0.000244140625$$