Question

simplify. express your answer using positive exponents.
$t^{-70}u \cdot t^{-1}u^{-1} \cdot t^{-3}u^{13}$

Explanation:

Step1: Combine like bases for \( t \)

When multiplying terms with the same base, add the exponents. For \( t \): \( t^{-70} \cdot t^{-1} \cdot t^{-3} = t^{-70 + (-1) + (-3)} = t^{-74} \)

Step2: Combine like bases for \( u \)

For \( u \): \( u^{1} \cdot u^{-1} \cdot u^{13} = u^{1 + (-1) + 13} = u^{13} \)

Step3: Convert negative exponent to positive

\( t^{-74} = \frac{1}{t^{74}} \)

Step4: Combine the results

The simplified form is \( \frac{u^{13}}{t^{74}} \)

Answer:

\(\frac{u^{13}}{t^{74}}\)