Question

simplify. express your answer using positive exponents. \\(\frac{3pq^{5}r}{3p^{0}q^{-1}r^{-4}}\\)

Explanation:

Step1: Simplify the coefficient and bases with the same variable using exponent rules.

For the coefficient: $\frac{3}{3} = 1$.
For the variable \( p \): Using the rule \( \frac{a^m}{a^n}=a^{m - n} \), we have \( \frac{p^1}{p^0}=p^{1 - 0}=p^1 = p \) (since \( a^0 = 1 \) for \( a
eq0 \)).
For the variable \( q \): \( \frac{q^5}{q^{-1}}=q^{5-(-1)}=q^{6} \).
For the variable \( r \): \( \frac{r^1}{r^{-4}}=r^{1-(-4)}=r^{5} \).

Step2: Multiply the simplified parts together.

Multiply the results from Step 1: \( 1\times p\times q^{6}\times r^{5}=pq^{6}r^{5} \).

Answer:

\( pq^{6}r^{5} \)