(y^9)(2y^2)^3

Question

The number following the ^ is an exponent.

Answer 1

Recall three of the laws of exponents I assume your teacher must have covered in your class:

i) x^mxⁿ = x^m+n

ii) (x^m)ⁿ = x^mn

iii) (xy)ⁿ = xⁿyⁿ

These two laws can be used here:

y⁹(2y²)³ = 2³y⁹y^2*3 = 8y⁹y⁶ = 8y⁹⁺⁶ = 8y¹⁵

 

Answer 2

Audy,

(y^9) the first term is y to the 9th power

(2y^2) is (y squared ) times 2.  Note that the exponent 2 does not apply to the factor 2.

(2y^2)^3 is the previous term raised to the 3rd power.  To see exactly how this calculates expand it:

   (2y^2)^3  =  (2y^2) *  (2y^2)  * (2y^2)

                   = 4*y^4  *  (2y^2)

                  =  8*y^6

  Go back and include the first term:

        (y^9)(2y^2)^3  =  (y^9) * 8*y^6

        (y^9)(2y^2)^3 = 8*y^15

There are two keys to this problem:

  Exponents add when their base numbers are multiplied.

  Observe which factors are raised to powers and which are not.

BruceS