Solve (2^3*2)^3div(2*2^4)^10

$$( 2 ^ { 3 } \times 2 ) ^ { 3 } \div ( 2 \times 2 ^ { 4 } ) ^ { 10 }$$

Evaluate

$$\frac{1}{274877906944}=3.637978807 \cdot 10^{-12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\left(2^{4}\right)^{3}}{\left(2\times 2^{4}\right)^{10}}$$

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

$$\frac{2^{12}}{\left(2\times 2^{4}\right)^{10}}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{2^{12}}{\left(2^{5}\right)^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 10 to get 50.

$$\frac{2^{12}}{2^{50}}$$

Rewrite 2^{50} as 2^{12}\times 2^{38}. Cancel out 2^{12} in both numerator and denominator.

$$\frac{1}{2^{38}}$$

Calculate 2 to the power of 38 and get 274877906944.

$$\frac{1}{274877906944}$$

Factor

$$\frac{1}{2 ^ {38}} = 3.637978807091713 \times 10^{-12}$$