a,b,c are nonzero real numbers....?

Question

and is a^3 b^5 c^6 = (a^2 c^6) / (3b^-1),
what is a equal to?


This a practice sat subject test 2 question and I dont know how to do it

Answer 1

The equation, as I understand you, is

a a a b b b b b c c c c c c =a a c c c c c c /(3 b^-1)

Because b^-1 b =1 and multiplication is the opposite of division, this is equivalent to

a a a b b b b b c c c c c c =a a c c c c c c /(3 b^-1) (3 (b^-1 b) /3)

So, because multiplication only isn't affected by brackets,

a a a b b b b b c c c c c c =a a c c c c c c /(3 b^-1) (3 b^-1) b /3

So

a a a b b b b b c c c c c c =a a c c c c c c b /3

So

a a a b b b b b c c c c c c 3 /3=a a c c c c c c b /3

So

a a a b b b b b c c c c c c 3 =a a c c c c c c b

So, because the order of multiplication of any series of numbers doesn't affect the result,

a a c c c c c c b (3 a b b b b) =a a c c c c c c b 1

So

3 a b b b b =1

So

a (3 b b b b) =1 /(3 b b b b) (3 b b b b)

So

a= 1 /(3 b b b b)

So

a= 1 /(3 b^4)

Answer 2

This just tests to see if you know how to manipulate powers. You can multiply and divide by powers of a, b, and c because they are nonzero, so that's where you use that fact.



First divide by c^6 on both sides, and the c terms cancel out to give you

a^3 b^5 = (a^2) / (3b^-1),



Divide by b^5 on both sides, and you get

a^3 = a^2 / 3b^4



Now divide by a^2 on both sides, and you get

a = 1 / 3b^4, which is the final answer.



1/3 is NOT the answer.

Answer 3

a^3 b^5 c^6 = (a^2 c^6) / (3b^-1)

a *b^5*(3b^-1)=1

3a *b^4=1

a=1/(3b^4)

Answer 4

I hope you can see the exponents.

a³ b⁵ c⁶ = (a² c⁶)/(3b⁻¹)

a³ b⁵ c⁶ = (a² c⁶)(3b)

a³ b⁵ c⁶ = 3a² b c⁶

a³ b⁵ = 3a² b

a b⁴ = 3

a = 3/(b⁴) = 3b⁻⁴