Question

Use the properties of exponents to simplify the expression.
(y3/2 x -1/2)^4

Answer 1

The properties of exponents used to simplify the expression are:

(a^m)^n = a^(m*n)

(a^m)^n = (a^n)^m

(a*b)^n = a^n * b^n

(a/b)^n = a^n / b^n

Using these properties, we can simplify the expression as follows:

(y3/2 x -1/2)^4

= (y^3/2 * x^-1/2)^4

= y^3/2 4 * x^-1/2 4

= y^(3/24) * x^(-1/24)

= y^6 * x^-2

So the simplified expression is: y^6 * x^-2