Simplify: `(-y^5 z^7)/(y^2 z^5)`

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msburch's profile pic

msburch | (Level 1) Adjunct Educator

Posted on

`(-y^5z^7)/(y^2z^5)` 

In this case, you must determine what bases are alike. you have y to the 5th power, which means you have y*y*y*y*y in the numerator. You have y to the 2nd power in the denominator y*y. You can cancel these out as values of 1 (y divided by y is equal to 1), or simply subtract these exponents. 

`y^5 -y^2 = y^3` you are left with `y^3` for the numerator. 

You must now simplify your terms with z as the base. The numerator is z to the 7th power, the denominator has z to the 5th power. You may subtract these for the same reason as above. You will simplify to z to the 2nd power. The negative sign in the beginning of the numerator is a multiple of -1. This means it will stay on the numerator. ``

we are left with `- y^3 z^2`

``

trevor1234rowe's profile pic

trevor1234rowe | (Level 2) eNoter

Posted on

`(-y^5z^7)/(y^2z^5) ` `= (-) * (y^2z^5)/(y^2z^5) * y^3z^2 = -1 * y^3z^2 = -y^3z^2`

a quick tip! whenever you divide two bases together, you subtract the exponents and keep the base! for example...

`x^3/x^2 = x^(3 - 2) = x^1 `

when you multiply two bases together you simply add the exponents, for example

`x^3 * x^2 = x^(2 + 3) = x^5 `

also, a good thing to remember, whenever you divide something by itself, it will always equal 1! even if it is an unknown variable!

`x/x = 1`

aishukul's profile pic

aishukul | Student, Grade 10 | (Level 3) Honors

Posted on

When you divide variables, instead of dividing, you subtract the exponents so it's: 

`-y^5-y^2= -y^3`

`z^7-z^5=z^2`

Also, since the exponents are larger on the top half of the fraction, when you subtract, the variables go on the top half, so the answer is:

`-y^3z^2.`

iamkaori's profile picture

iamkaori | Student, Grade 9 | (Level 2) Salutatorian

Posted on

start by identifying what each has in common. The numerator has:

-1*y*y*y*y*y*z*z*z*z*z*z*z

and the denominator is:

y*y*z*z*z*z*z

eliminate what they both in common. In this case, we can see that both contain:

y*y*z*z*z*z*z

divide both top and bottom by that.

Now the numerator will remain with:

-1*y*y*y*z*z

which equals to

-y^3z^2

while the denominator remains with 1.

Thus the final answer would be:

-y^3 z^2

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