To find an equivalent expression for [tex]\(\left(10 c^6 d^{-5}\right)\left(2 c^{-5} d^4\right)\)[/tex], we need to combine the terms step-by-step:
1. Multiply the constants:
[tex]\[
10 \times 2 = 20
\][/tex]
2. Combine the exponents for [tex]\(c\)[/tex]:
For [tex]\(c\)[/tex], we use the property of exponents [tex]\((a^m \cdot a^n = a^{m+n})\)[/tex].
[tex]\[
c^6 \times c^{-5} = c^{6 + (-5)} = c^1 = c
\][/tex]
3. Combine the exponents for [tex]\(d\)[/tex]:
For [tex]\(d\)[/tex], we again use the property of exponents [tex]\((a^m \cdot a^n = a^{m+n})\)[/tex].
[tex]\[
d^{-5} \times d^4 = d^{-5 + 4} = d^{-1}
\][/tex]
4. Simplify the expression:
Combining all these, we get
[tex]\[
20 c d^{-1} = \frac{20c}{d}
\][/tex]
Therefore, the equivalent expression is [tex]\(\boxed{\frac{20 c}{d}}\)[/tex].
Hence, the correct answer is:
A. [tex]\(\frac{20 c}{d}\)[/tex]
