What value of r makes  `y^28 = y^(3r) * y^7` true

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steveschoen's profile pic

steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

On the left, you can combine the exponents with addition.  So, the left becomes:

`y^(3r)` * `y^(7)` = `y^(3r+7)`

So, we have:

`y^(28)` = ` ` 

Since the bases are the same, the exponents have to be equal.  So, we have:

28 = 3r + 7

Solving this, we subtract 7 from each side then divide by 3 on each side:

28 = 3r + 7

  -7          -7

21 = 3r

` ``-:3`   ``    ` ` 

7 = r

So, r = 7

msburch's profile pic

msburch | (Level 1) Adjunct Educator

Posted on

The first thing you must do is check your bases. Are these like bases?
If so, check the operation. In this case you are multiplying. 
If you are multiplying, you can simply add the exponents together and keep the bases the same. 
Because of this rule, you can simplify this question to :

28 = 3r + 7

Use inverse operations to subtract 7 from both sides.

21 = 3r

Divide both sides by 3 to isolate the r variable.

21/3 = 3r/3

7 = r

In this case, your value is 7. 

aishukul's profile pic

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

Posted on

Just wanted to add on to the first step of the excellent answer above that whenever you are multiplying variables with exponents, you add the exponents together, and when you divide variables with exponents, you subtract the exponents. Just wanted to clarify this in case it wasn't clear. :)

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