Question

simplify. express your answer using positive exponents.
(6qrs⁵)(3q²rs⁴)

Explanation:

Step1: Multiply the coefficients

Multiply 6 and 3.
$6\times3 = 18$

Step2: Multiply the \( q \)-terms

Use the rule \( a^m \cdot a^n = a^{m + n} \). For \( q \) and \( q^2 \):
$q^1 \cdot q^2 = q^{1 + 2}=q^3$

Step3: Multiply the \( r \)-terms

For \( r \) and \( r \) (which is \( r^1 \)):
$r^1 \cdot r^1 = r^{1 + 1}=r^2$

Step4: Multiply the \( s \)-terms

For \( s^5 \) and \( s^4 \):
$s^5 \cdot s^4 = s^{5 + 4}=s^9$

Step5: Combine all terms

Multiply the results from Steps 1 - 4 together.
$18\times q^3\times r^2\times s^9 = 18q^3r^2s^9$

Answer:

\( 18q^3r^2s^9 \)