Final answer:
To simplify 9m5 multiplied by (-4m3), you multiply the coefficients (9*(-4)=-36) and add the exponents (5+3=8), resulting in -36m^8. which corresponds to option (a) -36m8.
Step-by-step explanation:
The question asks to simplify the expression 9m5 multiplied by (-4m3). When multiplying two exponential expressions with the same base, you add the exponents according to the property ma × mb = ma+b. So, to simplify this expression:
9m5 × (-4m3) = -36m5+3 = -36m8
To simplify the expression \(9m^5 \times (-4m^3)\), we will use the properties of exponents and multiplication. Here are the steps: 1. First, we multiply the coefficients (the numeric parts) of the two terms. In our expression, the coefficients are 9 and -4. \[9 \times -4 = -36\] 2.
Now we need to multiply the variables with exponents. To multiply the same base with exponents, we add the exponents. The base here is \(m\) with exponents of 5 and 3 from \(m^5\) and \(m^3\) respectively. \[m^5 \times m^3 = m^{5+3} = m^8\] 3.
Combining both the product of the coefficients and the product of the variables with exponents, we get the simplified expression: \[-36m^8\] Therefore, the correct answer is (a) \(-36m^8\).
This yields the simplified expression -36m8, which corresponds to option (a) -36m8.