Question

Simplify open parentheses x to the 5 eighths power close parentheses to the 2 thirds power.

Answer 1

`x^{(5)/(12)}`

Explanation:

`(x^{(5)/(8)})^{(2)/(3)}`

To simplify it we multiply the exponents inside with exponent outside

`(a^m)^n = a^(mn)`

`(5)/(8) *(2)/(3)`

Cancel out 8 and 2

`(5)/(4) *(1)/(3)`

`(5)/(12)`

tex](x^{\frac{5}{8}})^{\frac{2}{3}}=\frac{5}{12}[/tex]

Answer 2

If we are to express the word problem to its mathematical expression,

(x^5/8)^2/3

The concept to be used in order to answer this item is the product of the exponents. If,

(x^m)^n

The final answer would be,

x^mn

If we apply the same principle to the equation above,

(x^5/8)^(2/3)
x^(5/8)(2/3)
x^5/12
Thus, the most simplified form is equal to x^5/12.