Solve [frac{1}4^3]^3*[2^2]^2*[2*3]^2

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

Evaluate

$$\frac{9}{4096}\approx 0.002197266$$

Solution Steps

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

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

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

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

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

$$\frac{1}{262144}\times 2^{4}\times \left(2\times 3\right)^{2}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{1}{262144}\times 16\times \left(2\times 3\right)^{2}$$

Multiply \frac{1}{262144} and 16 to get \frac{1}{16384}.

$$\frac{1}{16384}\times \left(2\times 3\right)^{2}$$

Multiply 2 and 3 to get 6.

$$\frac{1}{16384}\times 6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{1}{16384}\times 36$$

Multiply \frac{1}{16384} and 36 to get \frac{9}{4096}.

$$\frac{9}{4096}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {12}} = 0.002197265625$$