Question

simplify. express your answer using positive exponents.
$\frac{6a^{5}b^{-2}c^{0}}{6ab^{-1}c^{-1}}$

Explanation:

Step1: Simplify the coefficient

The coefficients are both 6, and $\frac{6}{6}=1$.

Step2: Use the quotient - rule of exponents for $a$ terms

The quotient - rule states that $\frac{a^m}{a^n}=a^{m - n}$. For the $a$ terms, $\frac{a^5}{a}=a^{5-1}=a^4$.

Step3: Use the quotient - rule of exponents for $b$ terms

For the $b$ terms, $\frac{b^{-2}}{b^{-1}}=b^{-2-(-1)}=b^{-2 + 1}=b^{-1}=\frac{1}{b}$.

Step4: Use the quotient - rule of exponents for $c$ terms

For the $c$ terms, $\frac{c^0}{c^{-1}}$. Since $c^0 = 1$, then $\frac{1}{c^{-1}}=c^{0-(-1)}=c^1 = c$.

Step5: Combine the results

The simplified expression is $a^4\times\frac{1}{b}\times c=\frac{a^4c}{b}$.

Answer:

$\frac{a^4c}{b}$