Explanation:
especially when you deal with exponents, you need to write the problem properly.
either you can write them directly like
x⁵ or y²
or you use the "^" symbol for more complex exponents :
x^1/2 or y^-4/5
I assume the given problem is
(y^(3/2) x^(-1/2))⁴
remember the main rules for combining exponents :
multiplying the same base means adding the exponents :
x²×x⁶ = x⁸
exponent of exponent messages multiplying the exponents :
(x²)⁶ = x¹²
a negative exponent means 1/... :
x^-1 = 1/x, x^-2 = 1/x², ...
a fraction in an exponent means roots (based on the denominator of the fraction) :
x^(1/2) = sqrt(x) (square root)
x^(2/3) = cubic root(x²)
and also remember, an exponent always applies to the whole term (and all its parts).
(xy)⁵ = x⁵y⁵
so, now in our given problem we have the overall exponent of 4. we need to multiply that with the inner exponents :
y^(4×3/2) x^(4×-1/2) = y^(12/2) x^(-4/2) = y^6 x^-2 =
= y⁶/x²