#1**+1 **

There are two interpretations of this problem, and they both result in different answers, so I will address both. They are:

- \(32m*\frac{3}{4}m^2\)
- \(32m*(\frac{3m}{4})^2\)

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. |

TheXSquaredFactor
Jun 1, 2017

#1**+1 **

Best Answer

There are two interpretations of this problem, and they both result in different answers, so I will address both. They are:

- \(32m*\frac{3}{4}m^2\)
- \(32m*(\frac{3m}{4})^2\)

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. |

TheXSquaredFactor
Jun 1, 2017