Solve [(2^{3})^{4}]^{2}:(2^5)^2:(2^3)^3

$$[ ( 2 ^ { 3 } ) ^ { 4 } ] ^ { 2 } : ( 2 ^ { 5 } ) ^ { 2 } : ( 2 ^ { 3 } ) ^ { 3 }$$

Evaluate

$$32$$

Solution Steps

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

$$\frac{\frac{\left(2^{12}\right)^{2}}{\left(2^{5}\right)^{2}}}{\left(2^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 2 to get 24.

$$\frac{\frac{2^{24}}{\left(2^{5}\right)^{2}}}{\left(2^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{\frac{2^{24}}{2^{10}}}{\left(2^{3}\right)^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 24 to get 14.

$$\frac{2^{14}}{\left(2^{3}\right)^{3}}$$

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

$$\frac{2^{14}}{2^{9}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 9 from 14 to get 5.

$$2^{5}$$

Calculate 2 to the power of 5 and get 32.

$$32$$

Factor

$$2^{5}$$