How do I solve this? (8/125)^(-2/3)?

125/8 - because of the negative sign it is inverted.
5/2 - 3 as the denominator means you cube root it
25/4 - you square because of the 2 on 2/3

(8/125)^(-2/3)
= (2³/5³)^(-2/3)
= [(2/5)³]^(-2/3)
= (2/5)^[3×(-2/3)]
= (2/5)^(-2)
= (5/2)^2
= 5²/2²
= 25/4

(8/125)^(-⅔) = (2³/5³)^(-⅔)
= ((2/5)³)^(-⅔)
= (2/5)⁻²
= (5/2)²
= 25/4

(125/8)^(2/3) = (5/2)^2 = 25/4

(8/125)^(-2/3)
I would do the cube root part first
(2/5)^(-2)

Then squared
4/25^-1

Then invert
25/4

(8/125)^(-2/3)
= (125/8)^(2/3)
= (5/2)^2
= 25/4

= (8/125)^(- 2/3) → you know that: 8 = 2^(3)

= [2^(3)/125]^(- 2/3) → you know that: 125 = 5^(3)

= [2^(3)/5^(3)]^(- 2/3) → you can simplify

= [(2/5)^3]^(- 2/3) → you know that: (x^a)^(b) = x^(ab)

= (2/5)^[3 * - (2/3)] → you can simplify

= (2/5)^(- 2) → you know that: x^(- a) = 1/x^(+ a) = 1/x^(a)

= 1 / [(2/5)^(2)] → you know that: (a/b)^(x) = a^(x) / b^(x)

= 1 / [2^(2) / 5^(2)] → you can simplify

= 1 / [4/25] → you can simplify

= 25/4

The word "solve" is applied to equations and equations require an equals sign.
In this case "simplify" would be more appropriate.


125^(2/3)
----------------
8^(2/3)

5^2
--------
2^2

25
----- = 6 1/4
4

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