Question

Please answer. The end of my quarter ends today. I need my grades up.

Answer 1

Answer:

C.  $\frac{1}{15^4}$

Step-by-step explanation:

We must use the exponential adding rule in order to evaluate the product of these two exponents.

$\begin{document}\fbox{ \parbox{0.9\linewidth}{ \[ \textbf{Exponential Adding rule:} ~a^m \cdot a^n = a^{m + n} \] - \( a \): The base of the exponents. It must be the same for both. \\ - \( m \): The exponent in the term \( a^m \), representing the power to which the base \( a \) is raised. \\ - \( n \): The exponent in the term \( a^n \), representing the power to which the base \( a \) is raised. }}\end{document}$

As you can see, when you multiply two exponential terms with the same base, you add the exponents together.

Solving:

Apply exponential adding rule:

$(15^3)(15^{-7}) = 15^{3+(-7)$

$\text{Exponent:}~3+(-7) = \boxed{-4}$

$(15^3)(15^{-7}) = \boxed{15^{-4}}$

When you are given a negative exponent take the reciprocal with the positive exponent.

$15^{-4} = \frac{1}{15^4}$

Therefore, the correct answer option is C.