Question

How must I simplify this?

Answer 1

Simplify what?

Answer 2

Give me a sec

Answer 3

ok

Answer 4

\[\frac{ \sqrt[3]{a} }{\sqrt{5a} } . \frac{ a \sqrt{30} }{ \sqrt[3]{60a^2} }\]

Answer 5

There we go!

Answer 6

Okay, so first thing is first\[\Large\frac{a}{b}\cdot \frac{c}{d}=\frac{a\cdot c}{b\cdot d}\] Also: \[\Large\sqrt{a} \cdot \sqrt{b} = \sqrt{a\cdot b}\] Can you start with using these properties?

Answer 7

Yes, I see...

Answer 8

But what I did, was changing the square roots to powers of fractions

Answer 9

Alright, do you know the properties of exponents?

Answer 10

Where are you stuck?

Answer 11

Well, somewhere I had \[\frac{ 30a^\frac{ 11 }{ 6 } }{ 5a^\frac{ 1 }{ 2 } . (60a^\frac{ 7 }{ 3 }) }\]

Answer 12

I guess I probably multiplied the bottom part of that fraction totally wrong.

Answer 13

Remember that \[\Large x^{-n} = \frac{1}{x^n}\]

Answer 14

Yes, I know.

Answer 15

You need to keep your parenthesis when you converting roots into fractional exponents.

Answer 16

Oh, okay

Answer 17

Did I convert them correctly?

Answer 18

No, you messed up on parts

Answer 19

Oh... hmmm, which part

Answer 20

Well, the whole thing is kinda messy because you don't have parenthesis and such. But

Answer 21

\[\frac{ (a)^\frac{ 1 }{ 3} }{ (5a)^\frac{ 1 }{ 2 } } . \frac{ a(30)^\frac{ 1 }{ 2 } }{ (60a^2)^\frac{ 1 }{ 3 } }\]

Answer 22

How about that.

Answer 23

Good!

Answer 24

Okay :))

Answer 25

What I did after that, was something like this:

Answer 26

\[\frac{ (a)^\frac{ 4 }{ 3 } . (30)^\frac{ 1 }{ 2 } }{ (5a)^\frac{ 1 }{ 2 } . (60a^2)^\frac{ 1 }{ 3 } }\]

Answer 27

You can type \Large in front to make it more readable.

Answer 28

\[\frac{1}{8} + 1 = \frac{1}{8}+\frac{8}{8} = \frac{9}{8}\]