Solve frac{2^{4}*2^{7}*(2^2)^4}{2^2*2^-3}

$$\frac { 2 ^ { 4 } \cdot 2 ^ { 7 } \cdot ( 2 ^ { 2 } ) ^ { 4 } } { 2 ^ { 2 } \cdot 2 ^ { - 3 } }$$

Evaluate

$$1048576$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{2^{4}\times 2^{7}\times 2^{8}}{2^{2}\times 2^{-3}}$$

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\frac{2^{11}\times 2^{8}}{2^{2}\times 2^{-3}}$$

To multiply powers of the same base, add their exponents. Add 11 and 8 to get 19.

$$\frac{2^{19}}{2^{2}\times 2^{-3}}$$

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{2^{19}}{2^{-1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -1 from 19 to get 20.

$$2^{20}$$

Calculate 2 to the power of 20 and get 1048576.

$$1048576$$

Factor

$$2^{20}$$