To simplify the expression [tex]\(5 t^{-2} \cdot 2 t^{-5}\)[/tex], we'll take it step-by-step. We will handle the coefficients (numerical parts) and the exponents separately and then combine the results.
1. Handle the coefficients (numerical parts):
- The coefficients in the expression are 5 and 2.
- Multiply these coefficients:
[tex]\[ 5 \cdot 2 = 10 \][/tex]
2. Handle the exponents:
- The base of the exponents is [tex]\(t\)[/tex].
- The exponents in the expression are [tex]\(-2\)[/tex] and [tex]\(-5\)[/tex].
- Add the exponents together:
[tex]\[ -2 + (-5) = -2 - 5 = -7 \][/tex]
3. Combine the results:
- We now combine the numerical part with the variable and its new exponent. This gives us:
[tex]\[ 10 t^{-7} \][/tex]
After performing these steps, we have simplified the expression [tex]\(5 t^{-2} \cdot 2 t^{-5}\)[/tex] to [tex]\( 10 t^{-7} \)[/tex].
Among the given options, the correct answer is:
C. [tex]\(10 t^{-7}\)[/tex]
