Question

simplify. express your answer using positive exponents.
$r^{0}s^{-6}t \cdot rs^{-5}t^{-92} \cdot rst^{-36}$

Explanation:

Step1: Group like bases

Group terms with $r$, $s$, $t$ separately:
$(r^0 \cdot r \cdot r) \cdot (s^{-6} \cdot s^{-5} \cdot s) \cdot (t \cdot t^{-92} \cdot t^{-36})$

Step2: Apply exponent addition rule

For same bases, add exponents: $x^a \cdot x^b = x^{a+b}$

• For $r$: $r^{0+1+1} = r^2$
• For $s$: $s^{-6+(-5)+1} = s^{-10}$
• For $t$: $t^{1+(-92)+(-36)} = t^{-127}$

Combine results: $r^2 s^{-10} t^{-127}$

Step3: Convert to positive exponents

Use $x^{-a} = \frac{1}{x^a}$:
$r^2 \cdot \frac{1}{s^{10}} \cdot \frac{1}{t^{127}}$

Step4: Combine into single fraction

Multiply the terms:
$\frac{r^2}{s^{10} t^{127}}$

Answer:

$\frac{r^2}{s^{10}t^{127}}$