Question

simplify: $5b^2 \cdot 3b^7$
options: $15b^9$, $8b^9$, $8b^{14}$, $15b$ (last option partially visible)

Explanation:

Step1: Multiply coefficients

Multiply the coefficients \(5\) and \(3\): \(5\times3 = 15\).

Step2: Multiply variables (exponent rule)

For the variable \(b\), use the rule \(a^m\cdot a^n=a^{m + n}\). So \(b^{2}\cdot b^{7}=b^{2 + 7}=b^{9}\).

Step3: Combine results

Combine the coefficient and the variable: \(15\times b^{9}=15b^{9}\).

Answer:

\(15b^{9}\) (corresponding to the first option, e.g., A. \(15b^{9}\) if options are labeled that way)