Question

simplify. express your answer using positive exponents.
$\frac{3bc^{2}}{3b^{7}c^{5}}$

Explanation:

Step1: Divide the coefficients

The coefficients are 3 and 3. $\frac{3}{3}=1$.

Step2: Use the quotient - rule for exponents on $b$ terms

The quotient - rule for exponents is $\frac{a^m}{a^n}=a^{m - n}$. For the $b$ terms, we have $\frac{b}{b^7}=b^{1-7}=b^{- 6}=\frac{1}{b^6}$.

Step3: Use the quotient - rule for exponents on $c$ terms

For the $c$ terms, $\frac{c^2}{c^5}=c^{2 - 5}=c^{-3}=\frac{1}{c^3}$.

Step4: Combine the results

The simplified expression is $1\times\frac{1}{b^6}\times\frac{1}{c^3}=\frac{1}{b^6c^3}$.

Answer:

$\frac{1}{b^6c^3}$