Solve [(1/4)^{3}]^3*(2^3)^2*(2*3)^2

$$[ ( \frac { 1 } { 4 } ) ^ { 3 } ] ^ { 3 } \times ( 2 ^ { 3 } ) ^ { 2 } \times ( 2 \times 3 ) ^ { 2 }$$

Evaluate

$$\frac{9}{1024}\approx 0.008789062$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(\frac{1}{4}\right)^{9}\times \left(2^{3}\right)^{2}\times \left(2\times 3\right)^{2}$$

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

$$\left(\frac{1}{4}\right)^{9}\times 2^{6}\times \left(2\times 3\right)^{2}$$

Calculate \frac{1}{4} to the power of 9 and get \frac{1}{262144}.

$$\frac{1}{262144}\times 2^{6}\times \left(2\times 3\right)^{2}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{1}{262144}\times 64\times \left(2\times 3\right)^{2}$$

Multiply \frac{1}{262144} and 64 to get \frac{1}{4096}.

$$\frac{1}{4096}\times \left(2\times 3\right)^{2}$$

Multiply 2 and 3 to get 6.

$$\frac{1}{4096}\times 6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{1}{4096}\times 36$$

Multiply \frac{1}{4096} and 36 to get \frac{9}{1024}.

$$\frac{9}{1024}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {10}} = 0.0087890625$$