simplifing expressions divide

**andyboy179** · January 31st 2010, 03:04 AM

hi, i need to simplify 6a^3 x 2a^2
im not sure what i would do, i know i do 6/2=3 but i don't know what to do to the top numbers. can anyone help please?

**e^(i*pi)** · January 31st 2010, 03:38 AM

Originally Posted by andyboy179

hi, i need to simplify 6a^3 x 2a^2
im not sure what i would do, i know i do 6/2=3 but i don't know what to do to the top numbers. can anyone help please?

You've put times in your original question.

$6a^3 \times 2a^2 = (6)(2)a^{3+2} = 12a^5$

$\frac{6a^3}{2a^2} = \frac{6}{2} \cdot a^{3-2} = 3a^1 = 3a$

When dividing exponents [top numbers] you should subtract the bottom one from the top one

**andyboy179** · January 31st 2010, 09:49 AM

so if the question was 18a^-2 / 3a^-1 it would = 24a?

**e^(i*pi)** · January 31st 2010, 10:04 AM

Originally Posted by andyboy179

so if the question was 18a^-2 / 3a^-1 it would = 24a?

No it wouldn't.

$\frac{18a^{-2}}{3a^{-1}} = \frac{18}{3} \times a^{(-2)-(-1)}$

Another way

$\frac{18a^{-2}}{3a^{-1}} = \frac{18}{3} \times \frac{1}{a^2} \times a$

**andyboy179** · January 31st 2010, 10:06 AM

Originally Posted by e^(i*pi)

No it wouldn't.

$\frac{18a^{-2}}{3a^{-1}} = \frac{18}{3} \times a^{(-2)-(-1)}$

Another way

$\frac{18a^{-2}}{3a^{-1}} = \frac{18}{3} \times \frac{1}{a^2} \times a$

i don't really understand, would it be 8a?

**e^(i*pi)** · January 31st 2010, 10:11 AM

Originally Posted by andyboy179

i don't really understand, would it be 8a?

No, I don't know where you're getting 8 from. The number part is $\frac{18}{3} = 6$

For the exponent you're doing $-2 - (-1) = -2 + 1 = -1$

Therefore the answer is $6a^{-1}$ .

Since $a^{-1}$ is defined as $\frac{1}{a}$ then $\frac{6}{a}$ is equally correct

**andyboy179** · January 31st 2010, 10:15 AM

oh i understand now. cheers

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