another write in the form c (a^p) (b^q)

[CB1101]

__ab-a__
(b^2) -b

I have no idea how to start this problem, could someone give me a hint?

 

[HallsofIvy]

I would start with the obvious factoring: \(\displaystyle \frac{ab- a}{b^2- b}= \frac{a(b- 1)}{b(b- 1)}\).

 

[CB1101]

I would start with the obvious factoring: \(\displaystyle \frac{ab- a}{b^2- b}= \frac{a(b- 1)}{b(b- 1)}\).

ab^-1

 

[CB1101]

Could you help me with this one?

a^-1
(b^-1)​√a

 

[HallsofIvy]

ab^-1

Good!

 

[HallsofIvy]

Could you help me with this one?

a^-1
(b^-1)​√a

\(\displaystyle \sqrt{a}= a^{1/2}\) and \(\displaystyle 1/\sqrt{a}= a^{-1/2}\).

 

[mmm4444bot]

Have you learned the meaning of negative exponents?



Do you remember how to simplify a fraction divided by another fraction?

For example, can you simplify the following expression?

\(\displaystyle \dfrac{\frac{1}{7}}{\frac{1}{4}}\)



Also, do you remember how to rewrite a radical in exponential form?

For example, \(\displaystyle \sqrt{x} = x^{?}\)



You have not shown any attempt (or asked specific questions) on the second exercise, yet. I can't tell where you're stuck, but I can say that the skills above could help you rewrite that expression.

Please explain what you already know, and tell us where you're stuck. :cool:

 

[CB1101]

ab^-1

Have you learned the meaning of negative exponents?



Do you remember how to simplify a fraction divided by another fraction?

For example, can you simplify the following expression?

\(\displaystyle \dfrac{\frac{1}{7}}{\frac{1}{4}}\)



Also, do you remember how to rewrite a radical in exponential form?

For example, \(\displaystyle \sqrt{x} = x^{?}\)



You have not shown any attempt (or asked specific questions) on the second exercise, yet. I can't tell where you're stuck, but I can say that the skills above could help you rewrite that expression.

Please explain what you already know, and tell us where you're stuck. :cool:

I did what you said and here's my work:

a^-1
(b^-1) sqrt a

a^-1
(b^-1) a^1/2

(a^-1)(a^-1/2)(b)

(a^-2/3)(b)

Does that look correct?

 

[mmm4444bot]

(a^-1)(a^-1/2)(b)

(a^-2/3)(b)

Does that look correct?

Yes, that works, but the value in red is incorrect. A typo, perhaps?

 

[lookagain]

I did what you said and here's my work:

a^-1
(b^-1) sqrt a

a^-1
(b^-1) a^1/2

(a^-1)(a^-1/2)(b)

(a^-2/3)(b)

Does that look correct?

CB1101, there are two errors here. \(\displaystyle \ \ \)1) When the exponents of -1 and -1/2 are added together, the sum is equal to -2/2 + -1/2 = -3/2. \(\displaystyle \ \ \ \) 2) You must have grouping symbols around this fractional exponent when you write in this horizontal style, such as in "[a^(-3/2)]b, \(\displaystyle \ \ or \ \ \) "(a^(-3/2))b." \(\displaystyle \ \ \ \ \ \) Else, your incorrect portion of your answer of "a^-2/3" could be interpreted as \(\displaystyle \ \ \dfrac{a^{-2}}{3}.\) \(\displaystyle \ \ \ \) Likewise, "a^-3/2" could have been interpreted as \(\displaystyle \ \ \dfrac{a^{-3}}{2}.\)