Evaluate (2/105)^(a+2): Complex Fraction with Variable Exponent

Insert the corresponding expression:

$\left(\frac{2}{3\times7\times5}\right)^{a+2}=$

To solve the problem, we will leverage the rules of exponents:

• Apply the rule $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ to the expression $\left(\frac{2}{3\times7\times5}\right)^{a+2}$.
• Distribute the exponent $(a+2)$ to both the numerator and the denominator.

First, distribute the exponent to the numerator:

$2^{a+2}$

Now, distribute the exponent to the entire denominator:

$(3\times7\times5)^{a+2}$

Thus, the expression becomes:

$\frac{2^{a+2}}{(3\times7\times5)^{a+2}}$

This matches choice 3: $\frac{2^{a+2}}{\left(3\times7\times5\right)^{a+2}}$.