To simplify the expression [tex]\(\frac{c^{-6} d^4}{c^{-16} d^{14}}\)[/tex], let's follow these steps:
1. Combine the exponents of [tex]\(c\)[/tex]:
- The numerator has [tex]\(c^{-6}\)[/tex].
- The denominator has [tex]\(c^{-16}\)[/tex].
- When dividing powers of the same base, you subtract the exponent in the denominator from the exponent in the numerator.
- [tex]\[
c^{-6 - (-16)} = c^{-6 + 16} = c^{10}
\][/tex]
2. Combine the exponents of [tex]\(d\)[/tex]:
- The numerator has [tex]\(d^4\)[/tex].
- The denominator has [tex]\(d^{14}\)[/tex].
- When dividing powers of the same base, you subtract the exponent in the denominator from the exponent in the numerator.
- [tex]\[
d^{4 - 14} = d^{-10}
\][/tex]
So the simplified expression is:
[tex]\[
\frac{c^{-6} d^4}{c^{-16} d^{14}} = c^{10} d^{-10}
\][/tex]
The answer is not [tex]\(c^{10} d^{10}\)[/tex], [tex]\(c^2 d^2\)[/tex], nor [tex]\(\frac{d^{-2}}{d^{-2}}\)[/tex].
The correct simplified expression is:
[tex]\[
\frac{c^{10}}{d^{10}}
\][/tex]
Thus, the proper choice from the given options is:
[tex]\[
\frac{c^{10}}{d^{10}}
\][/tex]
