Question

simplify. express your answer using positive exponents.
\frac{9r^{-6}s^{-1}t^{0}}{3r^{-1}s^{9}t}

Explanation:

Step1: Divide the coefficients

$\frac{9}{3}=3$

Step2: Use exponent - subtraction rule for $r$

$r^{-6-(-1)} = r^{-6 + 1}=r^{-5}=\frac{1}{r^{5}}$

Step3: Use exponent - subtraction rule for $s$

$s^{-1 - 9}=s^{-10}=\frac{1}{s^{10}}$

Step4: Use exponent - subtraction rule for $t$

$t^{0 - 1}=t^{-1}=\frac{1}{t}$

Step5: Combine the results

$3\times\frac{1}{r^{5}}\times\frac{1}{s^{10}}\times\frac{1}{t}=\frac{3}{r^{5}s^{10}t}$

Answer:

$\frac{3}{r^{5}s^{10}t}$