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4X^5Z^3N^5
3X^2Y^4N^3
To find the solution go here
Fractions can get complicated enough on
their own, and so can Variables, but when you combine Variables into fractions
is when it gets even more complicated. Similar to previous methods when
simplifying expressions the easiest way to handle fractions with constants and
variables (1 or many) is to take it one part and step at a time. Start with
constants first, then go to Variables where you identify which ones are unique
and which variables appear multiple times. So if you had to simplify the
fraction "(15X^3N^5)/(3Y^4N^2)" to its simplest form, you would first look at
the constants, 15 and 3. Since 15 is on the top term (numerator) and 3 is on th
bottom term (denominator), it means that 15 is being divided by 3. So
'15/3'="5". 5 is the constant part of the result, and for easy reference,
realize that it is technically "5/1" and belongs either as a constant in front
of the fraction such as "5 * (X^3)/(Y^2)" or it can be placed on the
numerator. Now onto the variables. First thing to notice is that the "X" and
the "Y" variables are both unique, Next thing to notice is that the "X" is on
the numerator, while the "Y" is on the denominator. This means that since
they are unique, that they can stay in their original positions, the "X^3" in
the numerator and the "Y^4" in the denominator. The "N" variable is in both
the numerator and denominator. Now remember, when we multiplied the same
variables we added their powers, now when we are dividing the same variables
we subtract their powers. You must subtract the power of
the variable in the denominator from the power of the variable in the
numerator and the result would be in the numerator.So in this case we would
do "N^(5-2)". This would equal "N^3" and that is left on the numerator. So
the variable part of the answer would be "(X^3N^3)/(Y^4)" and therefore the
resultant could be written as
"5 * (X^3N^3)/(Y^4)" or as "(5X^3N^3)/(Y^4)".
To get a general step-by-step guide to solving fractions involving variables then go here.
Try this one out!
to get the solution click here.
To find out how to get the solution for this particular problem click here.
4X^5Z^3N^5
3X^2Y^4N^3
To find the solution go here
From the previous example in the previous paragraph, if you didn't want to have the "Y^4" in the denominator, but would rather have it moved to the numerator so you don't have to have a fraction then you can change it so that it is on the top. When a variable, or any number or binomial for that matter, that is raised to a power switches which part of the fraction it is in (numerator to denominator or denominator to numerator), the power which it is being raised to must be multiplied by "-1". So in the previous example where a "Y^4" was left in the denominator we could move it to the top of the fraction, and then get rid of the fraction all together. To do so we must multiply its power by "-1" and get it to be raised to the "-4" power. Now that it is raised to the "-4" power it is now on top of the fraction. That means another way to rewrite our previous answer would be "5X^3N^3Y^-4". Variables with negative powers still act the exact same with all the operations (adding, subtracting, multiplying and dividing) except that its power is now negative. This means that when you do "X^4 * X^-2" you still add the powers, but since the one power is negative you would be adding a negative, which is the same as subtracting it. Therefore, the resultant would be "X^2". With division, if you were to do "(X^6Y^4)/(X^-3)" the resultant would be "X^(6 - -3)Y^4". Since you are subtracting a negative number it is the same as adding the two powers which means the resultant would be "X^9Y^4".
When you get a problem where you are trying to multiply two complex
fractions that each involve variables, it can be simplified using these steps
by just multiplying them first, even if you end up with more than one of the
same variable in the numerator and/or denominator. An example of that would be:
And in case you want to know the answer to that problem then click here
To get help for this, step-by-step, then go here
Click next to continue on to binomials.
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