Question

I worked out this problem however, my answer is wrong. What did I do wrong?

5x^(2/3) (x^(1/3) + x^(-2/3))
³√((5x)²) × (x^(1/3) + x^(-2/3))
³√(25x³) + (³√(25x²))/(³√(x²))
My answer: x ³√(25) + ³√(25)

Correct Answer: 5x + 5

Answer 1

\[5x^{2/3}(x^{1/3} + x^{-2/3})\]
Open the parenthesis.
You'll get:
\[5x^{2/3}*x^{1/3} + 5x^{2/3}*x^{-2/3})\]
Which further gives us.
\[5x^{\frac{2}{3} + \frac{1}{3}} + 5x^{\frac{2}{3} - \frac{2}{3}}\]
Using the simple exponent rules. We have:
\[5x^1 + 5x^0 = 5x + 5 \]

Understood? :)

Answer 2

is there a parenthesis after the first 5?

Answer 3

\(\Large \bf 5x^{\frac{2}{3}}x^{\frac{1}{3}}+x^{-\frac{2}{3}}\qquad or\qquad (5x)^{\frac{2}{3}}x^{\frac{1}{3}}+x^{-\frac{2}{3}}\quad ?\)

Answer 4

@triciaal No, there isn't.
@AkashdeepDeb That makes much more sense, thank you very much! :D
@jdoe0001 It's more like the second one.

Thank you everyone for helping! :D

Answer 5

:)