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Simplify: 3nm^-2*m^(-4/3) * n^(-4/3)I need help figuring out this problem

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3nm^-2*m^(-4/3) * n^(-4/3)

I need help figuring out this problem

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mlsiasebs's profile pic

Posted (Answer #1)

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To simplify, we need to combine like variables.  When we are multiplying a like variable, we can add the powers for all instances of that variable.  Let's first look at our original formula


What we want to look at are all the n terms and combine their powers.

For n, we have powers of +1 (since the first n has no power, we assume it is 1) and -4/3.  Therefore the sum of the powers is -1/3.

For m, we have powers of -2 and -4/3.  We can rewrite -2 as -6/3 so that we can add it to -4/3 so we end up with -10/3. 

Now that we know the new powers, we can rewrite the expression combining the terms.


Since the powers are both negative, we can also write the variables as the denominator.


justaguide's profile pic

Posted (Answer #2)

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The expression `3nm^-2*m^(-4/3) * n^(-4/3)` has to be simplified.

Use the property `a^b*a^c = a^(b + c)`

`3nm^-2*m^(-4/3) * n^(-4/3)`

=> `3*n^1*n^(-4/3)*m^-2*m^(-4/3)`

=> `3*n^(1 - 4/3)*m^(-2 - 4/3)`

=> `3*n^(-1/3)*m^(-10/3)`

The simplified expression is `3*n^(-1/3)*m^(-10/3)`

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