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Use the properties of exponents to simplify the expression.(y 3/2 x -1/2)4

User BSG
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1 Answer

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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

User Shanker Paudel
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