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32m *  3/4 m(Squared) ? ¬ –¬

Guest Jun 1, 2017

#1
+815
+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
Sort:

#1
+815
+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
#2
+318
+1

Yeah!