Certainly! Let's simplify the expression [tex]\(18^{-4} \times 18^{-5}\)[/tex].
First, recognize that when you multiply two exponential expressions with the same base, you can add their exponents. This is based on the exponentiation rule:
[tex]\[a^m \times a^n = a^{m+n}\][/tex]
For our given expression:
[tex]\[18^{-4} \times 18^{-5}\][/tex]
We identify the base [tex]\(a = 18\)[/tex], and the exponents [tex]\(m = -4\)[/tex] and [tex]\(n = -5\)[/tex].
Next, we add the exponents together:
[tex]\[
-4 + (-5) = -4 - 5 = -9
\][/tex]
Thus,
[tex]\[18^{-4} \times 18^{-5} = 18^{-9}\][/tex]
Now, to interpret [tex]\(18^{-9}\)[/tex], recall that a negative exponent indicates the reciprocal. That is:
[tex]\[18^{-9} = \frac{1}{18^9}\][/tex]
However, the original question asked for the simplified form of the expression. Here, the calculations we performed lead us to:
[tex]\[18^{-4} \times 18^{-5} = 18^{-9}\][/tex]
The further numerical result of evaluating [tex]\(18^{-9}\)[/tex] is:
[tex]\[18^{-9} \approx 5.041357015064838 \times 10^{-12}\][/tex]
Thus, the simplified form of [tex]\(18^{-4} \times 18^{-5}\)[/tex] is [tex]\(18^{-9}\)[/tex] and its approximate value is [tex]\(5.041357015064838 \times 10^{-12}\)[/tex].
Therefore, none of the other given multiple-choice answers ([tex]\(18^{20}\)[/tex], [tex]\(\frac{1}{18^{20}}\)[/tex]) apply to this expression. The correct simplified form is:
[tex]\[18^{-9}\][/tex]
And again, just for emphasis on understanding values, the approximate numerical result is:
[tex]\[5.041357015064838 \times 10^{-12}\][/tex]
