Check my answer? Exponents

Question

Check my answer?  Exponents

abbles · Answer

Check all correct answers (there may be more than one).

In the expression a^b,
A. The value b is an exponent.
B. The value a tells you how many times to multiply b by itself.
C. The value a must be > 1.
D. The value b tells you how many times to multiply a by itself.
E. The value b must be an integer.

afloridagirl · Answer

a,d,e i believe

afloridagirl · Answer

i can explain if you want

calculusxy · Answer

With exponents you would have a base and the exponent itself. 

For example, in: 
$$\huge x^\color{red}{y}$$

$x$ is the `base`
$y$ is the `exponent`

abbles · Answer

I got A and D... why would E be correct?

afloridagirl · Answer

tbh i am probably wrng when it comes to saying its e

abbles · Answer

Hahh :P Well thanks for trying

afloridagirl · Answer

i have more of a gut feeling with that one, im sorry

calculusxy · Answer

E does not necessarily have to be an integer. 

It can be a fraction as well. 

For example: $2^{\frac{1}{2}}$

abbles · Answer

That's what I thought... so the only two that are correct are A and D?

whpalmer4 · Answer

exponents may be numbers other than integers.  for example$$x^{1/2}=\sqrt{x}$$

whpalmer4 · Answer

yes only A&D

calculusxy · Answer

Yes that is because you can take the format: 
$$\huge x^{\frac{a}{b}} = \sqrt[b]{x^a}$$

abbles · Answer

Okay, thanks everyone :)

calculusxy · Answer

You're welcome :)

calculusxy · Answer

@Abbles I just put the square root thing out there although it won't be of much importance to you if you're not a Algebra 2/Trig student.

abbles · Answer

Actually I'm in Precalc :P

calculusxy · Answer

Ok lol. Never mind so you get it :)

abbles · Answer

Haha yeah :) 
Do you mind checking one more exponent related question?

Simplify the expression below.  Write your answer with only positive exponents.
$$(a^2b^2c)/(a^5c^3) * (a^3b/c^4)$$

abbles · Answer

I got b^3/b^5

calculusxy · Answer

Let me check :) 

$$\frac{a^2b^2c}{a^5c^3} \times \frac{a^3b}{c^4} = a^{-3}b^2c^{-2} \times \frac{a^3b}{c^4} = \frac{b^2}{a^3c^2} \times \frac{a^3b}{c^4} = \frac{a^3b^3}{a^3c^6} = \frac{b^3}{c^6}$$

abbles · Answer

Woops, I meant b^3/c^5.

And I also did a typo on the question, it should be a^5c^2 on the denominator of the first term... but thanks for showing your work!  Looks all good.  :)

calculusxy · Answer

That's great!