Question

simplify. express your answer using positive exponents.
$3r^{2}s \cdot 10rs^{7}$

Explanation:

Step1: Multiply the coefficients

Multiply 3 and 10.
$3\times10 = 30$

Step2: Multiply the \( r \)-terms

Use the rule \( a^m \cdot a^n = a^{m + n} \) for \( r^2 \) and \( r \) (where \( r = r^1 \)).
$r^2 \cdot r = r^{2 + 1} = r^3$

Step3: Multiply the \( s \)-terms

Use the same exponent rule for \( s \) (where \( s = s^1 \)) and \( s^7 \).
$s \cdot s^7 = s^{1 + 7} = s^8$

Step4: Combine the results

Multiply the coefficient, \( r \)-term, and \( s \)-term together.
$30 \cdot r^3 \cdot s^8 = 30r^3s^8$

Answer:

\( 30r^3s^8 \)