Solve: 2^3 × 2^4 + (4^3)^2 + 2^5/2^3 - Complete Exponent Expression

Solve the following exercise:

$2^3\times2^4+(4^3)^2+\frac{2^5}{2^3}=$

We use the three appropriate power properties to solve the problem:

1. Power law for multiplication between terms with identical bases:

$a^m\cdot a^n=a^{m+n}$ 2. Power law for an exponent raised to another exponent:

$(a^m)^n=a^{m\cdot n}$ 3. Power law for the division of terms with identical bases:

$\frac{a^m}{a^n}=a^{m-n}$

We continue and apply the three previous laws to the problem:

$2^3\cdot2^4+(4^3)^2+\frac{2^5}{2^3}=2^{3+4}+4^{3\cdot2}+2^{5-3}=2^7+4^6+2^2$

In the first step we apply the power law mentioned in point 1 to the first expression on the left, the power law mentioned in point 2 to the second expression on the left, and the power law mentioned in point 3 to the third expression on the left, separately. In the second step, we simplify the expressions by exponents possession of the received terms,

Then,after using the substitution property for addition, we find that the correct answer is D.