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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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)`

mlsiasebs's profile pic

mlsiasebs | College Teacher | (Level 1) Associate Educator

Posted on

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

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

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.

`3n^(-1/3)m^(-10/3)`

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

`3/(n^(1/3)m^(10/3))` 

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