Question

3³m⁶·3⁵m¹³

Explanation:

Step1: Use exponent rule for multiplication (same base)

For bases with exponents, \(a^m \cdot a^n = a^{m + n}\). Apply this to the coefficients (base 3) and the variables (base m) separately.
For the coefficient part: \(3^3 \cdot 3^5 = 3^{3 + 5}\)
For the variable part: \(m^6 \cdot m^{13} = m^{6 + 13}\)

Step2: Calculate the exponents

Calculate \(3 + 5 = 8\) for the base 3, and \(6 + 13 = 19\) for the base m.
So we get \(3^8 \cdot m^{19}\)

Step3: Calculate \(3^8\) (optional, if numerical value is needed)

\(3^8 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 6561\)
So the simplified form is \(6561m^{19}\) (or \(3^8m^{19}\) if leaving in exponential form)

Answer:

\(3^8m^{19}\) (or \(6561m^{19}\))