Answer:
C. [tex]\frac{1}{15^4}[/tex]
Step-by-step explanation:
We must use the exponential adding rule in order to evaluate the product of these two exponents.
[tex]\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}[/tex]
As you can see, when you multiply two exponential terms with the same base, you add the exponents together.
Solving:
Apply exponential adding rule:
[tex](15^3)(15^{-7}) = 15^{3+(-7)[/tex]
[tex]\text{Exponent:}~3+(-7) = \boxed{-4}[/tex]
[tex](15^3)(15^{-7}) = \boxed{15^{-4}}[/tex]
When you are given a negative exponent take the reciprocal with the positive exponent.
[tex]15^{-4} = \frac{1}{15^4}[/tex]
Therefore, the correct answer option is C.