Solve (2*2^5)^3:(2^10*2)^2

$$( 2 \cdot 2 ^ { 5 } ) ^ { 3 } : ( 2 ^ { 10 } \cdot 2 ) ^ { 2 }$$

Evaluate

$$\frac{1}{16}=0.0625$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\left(2^{6}\right)^{3}}{\left(2^{10}\times 2\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{2^{18}}{\left(2^{10}\times 2\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$\frac{2^{18}}{\left(2^{11}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 11 and 2 to get 22.

$$\frac{2^{18}}{2^{22}}$$

Rewrite 2^{22} as 2^{18}\times 2^{4}. Cancel out 2^{18} in both numerator and denominator.

$$\frac{1}{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{1}{16}$$

Factor

$$\frac{1}{2 ^ {4}} = 0.0625$$