Question

simplify. express your answer using positive exponents.
$7p^4qr^4 \cdot 5p^5q^3r^8$

Explanation:

Step1: Multiply the coefficients

Multiply 7 and 5.
$7\times5 = 35$

Step2: Multiply the $p$ terms

Use the rule $a^m \cdot a^n = a^{m + n}$. For $p^4 \cdot p^5$, we add the exponents.
$p^4 \cdot p^5 = p^{4 + 5} = p^9$

Step3: Multiply the $q$ terms

Use the same exponent rule for $q^1 \cdot q^3$ (note that $q = q^1$).
$q^1 \cdot q^3 = q^{1 + 3} = q^4$

Step4: Multiply the $r$ terms

Use the exponent rule for $r^4 \cdot r^8$.
$r^4 \cdot r^8 = r^{4 + 8} = r^{12}$

Step5: Combine all terms

Multiply the results from Steps 1 - 4 together.
$35 \cdot p^9 \cdot q^4 \cdot r^{12} = 35p^9q^4r^{12}$

Answer:

$35p^9q^4r^{12}$