Solve 2(2^{5}*2^3:2^7)^4:2^3=

$$2 ( 2 ^ { 5 } \cdot 2 ^ { 3 } : 2 ^ { 7 } ) ^ { 4 } : 2 ^ { 3 } =$$

Evaluate

$$4$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{2\times \left(\frac{2^{8}}{2^{7}}\right)^{4}}{2^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 8 to get 1.

$$\frac{2\times \left(2^{1}\right)^{4}}{2^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 1 and 4 to get 4.

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

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

$$\frac{2^{5}}{2^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

$$2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4$$

Factor

$$2^{2}$$