Question

simplify. express your answer using positive exponents.
$10p^{3}q\cdot 7p^{6}q$

Explanation:

Step1: Multiply the coefficients

Multiply 10 and 7.
\(10\times7 = 70\)

Step2: Multiply the \(p\)-terms using exponent rule

Use \(a^m \cdot a^n = a^{m + n}\) for \(p^3 \cdot p^6\).
\(p^3 \cdot p^6 = p^{3+6}=p^9\)

Step3: Multiply the \(q\)-terms using exponent rule

Use \(a^m \cdot a^n = a^{m + n}\) for \(q \cdot q\) (note \(q = q^1\)).
\(q \cdot q = q^{1 + 1}=q^2\)

Step4: Combine the results

Multiply the coefficient, \(p\)-term, and \(q\)-term together.
\(70\times p^9\times q^2 = 70p^9q^2\)

Answer:

\(70p^9q^2\)