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 32m *  3/4 m(Squared) ? ¬ –¬ 

Guest Jun 1, 2017

Best Answer 

 #1
avatar+2139 
+1

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

 

  1. \(32m*\frac{3}{4}m^2\)
  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
avatar+2139 
+1
Best Answer

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

 

  1. \(32m*\frac{3}{4}m^2\)
  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
 #2
avatar+473 
+1

Yeah!

AsadRehman  Jun 1, 2017
 #3
avatar
0

[Question Publisher] Thank you so much I now under stand! laugh

Guest Jun 1, 2017

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