Question

simplify. express your answer using positive exponents. 9a^2 * 9a^9

Explanation:

Step1: Apply exponent - product rule

When multiplying two terms with the same base \(a^m\cdot a^n=a^{m + n}\), and for a constant \(c\), \(c^m\cdot c^n=c^{m + n}\). Here the base for the constant is 9 and for the variable is \(a\).
\[9^{2}\cdot9^{9}\cdot a^{9}\cdot a^{9}=9^{2 + 9}\cdot a^{9+9}\]

Step2: Calculate the exponents

Calculate \(2 + 9\) for the exponent of 9 and \(9+9\) for the exponent of \(a\).
\[9^{2 + 9}\cdot a^{9+9}=9^{11}\cdot a^{18}\]

Answer:

\(9^{11}a^{18}\)