Simplify the Expression: a^(7+x)/a^(10-2x) Using Exponent Rules

Note that in this problem there is a fraction where both the numerator and denominator contain terms with identical bases, therefore we will use the division law between terms with identical bases to solve the exercise:

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

Let's apply the aforementioned law:

$\frac{a^{7+x}}{a^{10-2x}}=a^{7+x-(10-2x)}$

In the first stage, we directly used the above exponents law and performed a simple subtraction between the exponent of the term in the numerator and the exponent of the term in the denominator, while using a common base. Since the term's exponent in the denominator is a two-term algebraic expression, we performed the subtraction carefully using parentheses.

We'll continue by simplifying the exponential expression, and use the distribution law to expand the parentheses, while remembering that the (-) sign before the parentheses is actually multiplication by minus 1:

$a^{7+x-(10-2x)}=a^{7+x-10+2x}=a^{-3+3x}$

where in the second stage we combined like terms in the exponent.

We obtained the most simplified expression, so we are done.

Therefore, the correct answer is B.