Question

simplify. express your answer using positive exponents. $8b^{7}c^{3} \cdot 5b^{9}c \cdot 3b^{7}c$

Explanation:

Step1: Multiply the coefficients

Multiply 8, 5, and 3. So, \(8\times5\times3 = 120\).

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

For \(b^7 \cdot b^9 \cdot b^7\), use the rule \(a^m \cdot a^n = a^{m + n}\). So, \(7+9 + 7=23\), thus \(b^{23}\).

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

For \(c^3 \cdot c \cdot c\), note that \(c = c^1\), so using \(a^m \cdot a^n = a^{m + n}\), we get \(3 + 1+ 1 = 5\), thus \(c^5\).

Step4: Combine all parts

Combine the coefficient, \(b\)-term, and \(c\)-term.

Answer:

\(120b^{23}c^5\)