+2446 There are two interpretations of this problem, and they both result in different answers, so I will address both. They are:
I believe that you mean problem #1, but I'll solve both anyway. It's good practice:
| \(32m*\frac{3}{4}m^2\) | This is the original equation. To simplify, evaluate the coefficients and variables separately. I opted to deal with the variable first. We'll use this exponent rule: \(m^a*m^b=m^{a+b}\) |
| \(32m^3*\frac{3}{4}\) | Now, multiply 32 by 3/4 and simplify fully |
| \(\frac{32m^3*3}{4}\) | Do 32*3 first |
| \(\frac{96m^3}{4}\) | Do 96/4 |
| \(24m^3\) | This is your answer for interpretation #1 |
Now, let's do interpretation #2:
| \(32m*(\frac{3m}{4})^2\) | This is the original equation in scenario #2. First, square 3m/4. Remember that \((\frac{a}{b})^2=\frac{a^2}{b^2}\) |
| \(32m*\frac{(3m)^2}{4^2}\) | Simplify the numerator and denominator. |
| \(\frac{32m}{1}*\frac{9m^2}{16}\) | Instead of doing 32*9, let's notice that 32 and 16 can be canceled out! This simplifies matters a lot! |
| \(\frac{2m}{1}*\frac{9m^2}{1}={2m}*{9m^2}\) | Use the exponent rule that states that \(a^b*a^c=a^{b+c}\) |
| \(2m^3*9\) | Multiply 2*9, which is 18, of course |
| \(18m^3\) | This is your final answer for interpretation #2. |
+2446
Evaluating this requires knowledge of the fraction rules. Here it is step-by-step
| \(\frac{-5}{\frac{4}{3}}\) | This is the original expression. Let's apply a rule with fractions that says that \(\frac{a}{\frac{b}{c}}=\frac{ac}{b}\hspace{1mm},b\neq0,c\neq0\) |
| \(\frac{-5*3}{4}\) | Using the rule above, the problem becomes simpler to understand and solve |
| \(\frac{-15}{4}=-3.75\) | |
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