Question

simplify. assume that no variable equals 0.
$t^9 \cdot t^{-8}$
\bigcirc $2t$
\bigcirc $t^{-72}$
\bigcirc $t^{17}$
\bigcirc $t$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying two powers with the same base, we add the exponents. The rule is \(a^m \cdot a^n = a^{m + n}\), where \(a\) is the base and \(m,n\) are exponents. Here, the base \(a = t\), \(m = 9\) and \(n=- 8\).

Step2: Apply the exponent rule

For \(t^{9}\cdot t^{-8}\), we add the exponents: \(9+(-8)=9 - 8 = 1\). So \(t^{9}\cdot t^{-8}=t^{1}=t\).

Answer:

The correct option is the one with \(t\), so the answer is the last option (the one with \(t\) as the choice, assuming the options are ordered as given: the fourth option which is \(t\)). If we list the options as per the original: the last option (let's say the fourth option is \(t\), so the answer is the option labeled with \(t\), for example, if the options are:

A. \(2t\)

B. \(t^{-72}\)

C. \(t^{17}\)

D. \(t\)

Then the answer is D. \(t\)