simplify.\n\frac{3a^{5}b^{-6}c^{2}}{18a^{-3}c^{-4}}\nwrite your answer using only positive exponents.
simplify.\n\frac{3a^{5}b^{-6}c^{2}}{18a^{-3}c^{-4}}\nwrite your answer using only positive exponents.
Answer
Explanation:
Step1: Simplify the coefficient
Divide 3 by 18 to get $\frac{3}{18}=\frac{1}{6}$.
Step2: Apply the quotient - rule for exponents with the same base ($a^m\div a^n=a^{m - n}$) for $a$ terms
$a^{5}\div a^{-3}=a^{5-(-3)}=a^{8}$.
Step3: Deal with the $b$ term
The $b$ term in the numerator is $b^{-6}$, and since there is no $b$ term in the denominator, it remains as $b^{-6}=\frac{1}{b^{6}}$ in positive - exponent form.
Step4: Apply the quotient - rule for exponents with the same base ($c^m\div c^n=c^{m - n}$) for $c$ terms
$c^{2}\div c^{-4}=c^{2-(-4)}=c^{6}$.
Step5: Combine the terms
Multiply the simplified coefficient and the terms with variables: $\frac{1}{6}\times a^{8}\times\frac{1}{b^{6}}\times c^{6}=\frac{a^{8}c^{6}}{6b^{6}}$.
Answer:
$\frac{a^{8}c^{6}}{6b^{6}}$