Question

simplify. express your answer using positive exponents.
$\frac{9r^{-4}s^{-7}t^{-1}}{r^{-6}s^{0}t^{-1}}$

Explanation:

Step1: Use exponent - division rule

When dividing like - bases $a^m\div a^n=a^{m - n}$, and any non - zero number to the power of 0 is 1 ($a^0 = 1,a
eq0$).
$\frac{9r^{4}s^{-7}t^{-1}}{r^{-6}s^{0}t^{-1}}=9r^{4-(-6)}s^{-7 - 0}t^{-1-(-1)}$

Step2: Simplify the exponents

$4-(-6)=4 + 6=10$, $-7-0=-7$, $-1-(-1)=-1 + 1 = 0$.
So we have $9r^{10}s^{-7}t^{0}$.
Since $t^{0}=1$, the expression becomes $9r^{10}s^{-7}$.

Step3: Rewrite with positive exponents

Using the rule $a^{-n}=\frac{1}{a^{n}}$, we get $\frac{9r^{10}}{s^{7}}$.

Answer:

$\frac{9r^{10}}{s^{7}}$