Stuck with exponents no clue what to do ?

[plucky ivy]

Is it multiple choice?

[twin heath]

yeah

well it shows the answer but i still dont understand how it is solved

[plucky ivy]

So if you have a fraction in the denominator like 10c⁴/3b³, it's the same thing as 1/(10c⁴/3b³), so you can just flip the fraction so it becomes 3b³/10c⁴
After that you multiply it with 2mc²/6b, since b>0 and c>0, 3b and 2c² cancels out, leaving you with the answer

[twin heath]

didnt understood after flipping the fraction

[plucky ivy]

After flipping the fraction we get 3b³/10c⁴ • 2mc²/6b. We can multiply these two together and get 6b³mc²/60c⁴b. Then cancel out 6, c², and b to get mb²/10c²

Sorry in my original explanation i wrote m²

[twin heath]

wait how did we got 6b^3mc^2

@plucky ivy

[plucky ivy]

We got it by multiplying 3b³ with 2mc², remember that multiplication is commutative, so multiplying the denominators together is completely fine

[twin heath]

ty its done

ive another doubt btw

[plucky ivy]

Np

[plucky ivy]

What is it

[twin heath]

$5^{^{\scriptsize \dfrac{1}{3}}}-5^{^{\scriptsize \dfrac{4}{3}}}$

[arctic glen]

Urara4ya

[twin heath]

how to solve this

[plucky ivy]

Are you looking to simplify?

[twin heath]

yeah

[plucky ivy]

You could factor out 5^⅓ to get 5^⅓(1 - 5⁴) then simplify the part inside the bracket and multiply the result by 5^⅓

Or perhaps you're looking for a different form

[twin heath]

wait

lemme send u the ques

[plucky ivy]

Oh yea, my bad

It's supposed to be 5^⅓(1-5)

So factor out 5^⅓ from 5^⅓ and 5^(4÷3), so you'll get 5^⅓(1 - 5^(3÷3))

[twin heath]

and how to do that exactly

[twin heath]

@plucky ivy

[plucky ivy]

Do which part

Are you confused about the factoring part?

[twin heath]

yeah

[twin heath]

about the factoring part

[plucky ivy]

So if you're factoring something out, you are essentially dividing the term by what you're factoring, so for example, 16, if you want to factor 2 out, you have to divide the term by 2, so it becomes 2(8). For exponents, division is the same as subtraction, shown in the identity a^b ÷ a^c = a^(b - c).
So that means if we want to factor out 5^⅓, we're going to have to divide the terms by 5^⅓. So 5^⅓ ÷ 5^⅓ is just 1, and 5^(4÷3) ÷ 5^⅓ is 5^((4÷3) - ⅓), which is just 5^(3÷3)

[twin heath]

ohh