Question

I am unsure as to writing some of the functions on here. But here goes:
Simplify:
3√125(x-10)3 Both the 3's are supposed to be exponents.

Answer 1

You mean this?\[\Huge \sqrt[3]{125(x-10)^3}\]

Answer 2

Yes!

Answer 3

Note: 125 = 5³

Answer 4

Break it into \[\Huge \sqrt[3]{125} \cdot \sqrt[3]{(x-10)^3}\]

Answer 5

So when simplifying it would be ^3√5^3(x-10)^3

Answer 6

Ohhhh I see

Answer 7

Yeah, and you can simplify it ever more.

Answer 8

Is this clear?

Answer 9

^3√5^3*^3√(x-10)^3 ????

Answer 10

@Helenshouse It shows that you don't see clearly :)

Answer 11

How are you showing ^3 ? Is there a short key to write this?

Answer 12

Sigh, no but I sure am trying!

Answer 13

Let me show you an example. \[\Large \sqrt[5]{a^5} = a \text{ because } a^5 = a \cdot a \cdot a \cdot a \cdot a\]

Now, what is \[\huge \sqrt[3]{5^3}\] and \[\Large \sqrt[3]{(x-10)^3}\]

Answer 14

The first is ^3√125 right?

Answer 15

The second is ^3√(x-10)^3 I am unsure........

Answer 16

No, I mean simplify it.

Answer 17

@Helenshouse Let me put this way, can you convert cube root into exponent?

Answer 18

Do you know any exponent properties?

Answer 19

^3√125*(x-10)^3

Answer 20

No, don't combine them. It makes it worse. Here, let me show you.

√25 = √5² = 5, right? Do you know why?

Answer 21

I am looking in my notes.

Answer 22

Yes 5*5=25

Answer 23

√25 = √5² = 5
Similarly, ³√ 125 = ....?

Answer 24

5^3

Answer 25

I am so lost here

Answer 26

You missed my point, what we're looking for is ³√ 125 ( not 125)

Answer 27

Ok

Answer 28

Let try again filling the second line by following the first line:
√25 = √5² = 5
Similarly, ³√ 125 = .... = ...

Answer 29

√5^3 = 5*5*5 I'm not sure

Answer 30

Do you understand that √5² = (5²)^( 1/2) ?

Answer 31

I think it is ^3√5^3