Question

Evaluate this exponential expression.
(0.125)^2/3

Answer 1

it easy

Answer 2

what would be 0.125 as a fraction?

Answer 3

so... let us convert to a fraction first
let's see what we get

Answer 4

1/8

Answer 5

@jdoe0001 Now what?

Answer 6

ohhh haemm ok one sec

Answer 7

Answer choices:
0.0025
0.025
0.25

Answer 8

\(\large {
(0.125)^{\frac{2}{3}}\implies \left( \cfrac{1}{8} \right)^{\frac{2}{3}}
\\ \quad \\
{\color{brown}{ 8=2^3}}\quad and\quad a^{-{\color{red} n}} \implies \cfrac{1}{a^{\color{red} n}}\qquad \qquad

\cfrac{1}{a^{\color{red} n}}\implies a^{-{\color{red} n}}\quad thus
\\ \quad \\
\left( \cfrac{1}{8} \right)^{\frac{2}{3}}\implies \left( \cfrac{1}{{\color{brown}{ 2^3}}} \right)^{\frac{2}{3}}\implies (2^{{\color{red}{ -3}}})^{\frac{2}{3}}\implies 2^{{\color{red}{ \cancel{-3}}}\frac{2}{\cancel{3}}}\implies ?
}\)

Answer 9

What?

Answer 10

anything you don't follow there?

Answer 11

Idk the answer. What is it? Lol

Answer 12

well.. you tell us
what is it?

Answer 13

Here's the answer choices:
0.0025
0.025
0.25

Answer 14

None of your work shows anything like the answer choices.

Answer 15

so.. what does \(\large {
(0.125)^{\frac{2}{3}}\implies \left( \cfrac{1}{8} \right)^{\frac{2}{3}}
\\ \quad \\
{\color{brown}{ 8=2^3}}\quad and\quad a^{-{\color{red} n}} \implies \cfrac{1}{a^{\color{red} n}}\qquad \qquad

\cfrac{1}{a^{\color{red} n}}\implies a^{-{\color{red} n}}\quad thus
\\ \quad \\
\left( \cfrac{1}{8} \right)^{\frac{2}{3}}\implies \left( \cfrac{1}{{\color{brown}{ 2^3}}} \right)^{\frac{2}{3}}\implies (2^{{\color{red}{ -3}}})^{\frac{2}{3}}\implies 2^{{\color{red}{ \cancel{-3}}}\cdot \frac{2}{\cancel{3}}}\implies ?
}\)

give you?

Answer 16

I have no idea

Answer 17

the choices are not meant to be a menu to choose from

they're just a guideline

so... simplify that, see what you get, and the choices must reflect that

Answer 18

Not really. It has to be one of them.

Answer 19

Idk what you're meaning by any of that.

Answer 20

well... you're expected to have studied all that by now, otherwise, makes no sense to give you the exercise

Answer 21

I do online school so yeah. I'm just now learning it and the way you're explaining it doesn't make sense.

Answer 22

unless you're expected to use the calculator
and you may well could do that I gather

Answer 23

2*2=4. That's what I got from your drawing.

Answer 24

Is 4 one of the answer choices? Nope.

Answer 25

2*2? hmmm
well..... ok.... do you see how we got the \(2^3\) and then the \(2^{-3} ?\)

Answer 26

No.

Answer 27

ok
how about this part \(\large {\color{brown}{ 8=2^3}}\quad and\quad a^{-{\color{red} n}} \implies \cfrac{1}{a^{\color{red} n}}\qquad \qquad

\cfrac{1}{a^{\color{red} n}}\implies a^{-{\color{red} n}}
\)

anything confusing there?

Answer 28

Yup.

Answer 29

You're not using any of the numbers in MY equation. Lol

Answer 30

ok... what part? is just notation, I understand

hehe

Answer 31

Any of it. Can you lead me to the answer or no?

Answer 32

well... the idea being

\(\large and\quad a^{-{\color{red} n}} \implies \cfrac{1}{a^{\color{red} n}}\qquad \qquad

\cfrac{1}{a^{\color{red} n}}\implies a^{-{\color{red} n}}\)

do you follow what that means?

means, a number, with a negative exponent, could also be written as the same number
with a positive exponent but under 1
or the other way around

so any number with whatever exponent, could be rewritten as the same number, as denominator, with the exponent as negative

Answer 33

But what about MY problem?

Answer 34

dohh.. . rather what's \(\large 2^3=?\)

Answer 35

8

Answer 36

so... we know that \(\large 8= 2^3\)

and we also know that we could write 1/8 as \(\cfract{1}{2^3}\)

and we also know we could write \(\bf \cfrac{1}{2^3}\implies 2^{-3}\)

so \(\bf (0.125)^{\frac{2}{3}}\implies \left( \cfrac{1}{8} \right)^{\frac{2}{3}}
\\ \quad \\
{\color{brown}{ 8=2^3}}\quad and\quad a^{-{\color{red} n}} \implies \cfrac{1}{a^{\color{red} n}}\qquad \qquad

\cfrac{1}{a^{\color{red} n}}\implies a^{-{\color{red} n}}\quad thus
\\ \quad \\
\left( \cfrac{1}{8} \right)^{\frac{2}{3}}\implies \left( \cfrac{1}{{\color{brown}{ 2^3}}} \right)^{\frac{2}{3}}\implies (2^{{\color{red}{ -3}}})^{\frac{2}{3}}\)

follow that?

Answer 37

Nope

Answer 38

hmmm so.. how are you expected to evaluate it then?

I gather you haven't covered this section yet of negative exponentials

so. what section is this exercise meant to cover?

are you simply supposed to use the calculator? because you could do that too

Answer 39

well...then you don't need help with it

at least not as most folks here define it

Answer 40

I do need help. You're just not very good at explaining it, obviously.

Answer 41

Since I still don't understand it.