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

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

Evaluate

$$9437184$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

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

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

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

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

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

Calculate 4 to the power of 6 and get 4096.

$$4096\times 2^{6}\times \left(2\times 3\right)^{2}$$

Calculate 2 to the power of 6 and get 64.

$$4096\times 64\times \left(2\times 3\right)^{2}$$

Multiply 4096 and 64 to get 262144.

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

Multiply 2 and 3 to get 6.

$$262144\times 6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$262144\times 36$$

Multiply 262144 and 36 to get 9437184.

$$9437184$$

Factor

$$2^{20}\times 3^{2}$$