The number following the ^ is an exponent.

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

# 2 Answers

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

i) x^{m}x^{n} = x^{m+n}

ii) (x^{m})^{n} = x^{mn}

iii) (xy)^{n} = x^{n}y^{n}

These two laws can be used here:

y^{9}(2y^{2})^{3} = 2^{3}y^{9}y^{2*3} = 8y^{9}y^{6} = 8y^{9+6} = 8y^{15}

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:

= 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*