SOLUTION: PLease help to simplify m^x/3*n^3x Divided by m^2x*n^3x/4

SOLUTION: PLease help to simplify m^x/3n^3x Divided by m^2xn^3x/4

Question 68259This question is from textbook An Incremental Development
: PLease help to simplify
m^x/3*n^3x
Divided by
m^2x*n^3x/4
This question is from textbook An Incremental Development

Answer by rmromero(383) (Show Source): You can put this solution on YOUR website!
Solution

Step 1: Following the Property of Exponents for division which states that, For all real numbers, a (refers to the base), a is not equal to 0 and for all positive integers x and y:
If x > y then m^x divided by m^y = m^x-y
If x < y then m^x divided by m^y = 1 / m^y-x
Note: you can apply this property with the same base
From the expression
m^x/3*n^3x
Divided by
m^2x*n^3x/4
the exponent 3x > 3x/4 so we are going to write
n^3x-3x/4
and since x/3 < 2x, we are going to write
1 divided by m^2x-x/3
therefore we have
n^3x-3x/4
divided by
m^2x-x/3

Step 2:Applying Subtraction of mixed expression, multiply 4 to the exponent 3x and 3x/4
n^(12x-3x)/4
multiply 3 to the exponent 2x and x/3
m^(6x-x)/3
so we have
n^(12x-3x)/4
divided by
m^(6x-x)/3

Step 3: Combine like terms 12x - 3x = 8x and copy the denominator which is 4.
n^8x/4
Combine 6x - x = 5x and copy the denominator 3
m^5x/3
Then we will have
n^8x/4
divided by
m^5x/3

Step 4: Simplify the exponent of the numerator 8x/4 by dividing both by 2 getting a result 2x.Since the exponent of the denominator cannot be simplified, write it as it is 5x/3
n^2x
divided by
m^5x/3

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