Need help simplfying some expressions

Laura901 · #1 $Old$ August 11th, 2008, 08:44 AM

81 x ^10 y^6 divided by (3x^2 y) ^4

6x+18 over x plus 3

12c^2 divided by 3c +6

Dubulus · #2 $Old$ August 11th, 2008, 08:49 AM

Quote:

Originally Posted by Laura901 $View Post$

81 x ^10 y^6 divided by (3x^2 y) ^4

6x+18 over x plus 3

12c^2 divided by 3c +6

1. start by expanding the bottom...

3^4 * (x^2)^4 * y^4 =
81x^8y^4

now cancel like terms
the 81 is removed completely
x^10/x^8 = x^2
y^6/y^4 = y^2

final answer: x^2 * y^2

Simplicity · #3 $Old$ August 11th, 2008, 09:00 AM

Quote:

Originally Posted by Laura901 $View Post$

81 x ^10 y^6 divided by (3x^2 y) ^4

6x+18 over x plus 3

12c^2 divided by 3c +6

I will provide you with rules through which you will be able to conduct the questions.
__________________

$\frac{81x^{10}y^{6}}{(3x^2y)^4}$

Use these rules:
$(x^ay^b)^c = x^{ac}y^{bc}$
$\frac{a^xb^y}{a^sb^t} = a^{x-s}b^{y-t}$

Use the rules stated above then simplify the expression.
__________________

$\frac{6x+18}{x + 3}$

Use this rule:
Factorising $ax+bx = x(a+b)$

Factorise the numerator and then simplify the expression.
__________________

$\frac{12c^2}{3c +6}$

Use this rule:
Factorising $ax+bx = x(a+b)$

Factorise the denominator and then simplify the expression.

Quick · #4 $Old$ August 11th, 2008, 09:01 AM

Quote:

Originally Posted by Laura901 $View Post$

12c^2 divided by 3c +6

$\frac{12c^2}{3c+6}=\frac{ 3\cdot 4c^2}{3(c+2)} =\frac{\not 3\cdot 4c^2}{\not 3(c+2)} = \frac{4c^2}{c+2}$