Answer:
Expression 1, 2 and 3 uses the correct exponential properties.
Step-by-step explanation:
Some of the properties of exponents are:
[tex]a^{-m} = \displaystyle\frac{1}{a^m}\\\\(a^m)^n = a^{mn}\\\\\frac{a^m}{a^n} = a^{m-n}\\\\a^m\times a^n = a^{m+n}[/tex]
We have to check the expressions with correct properties of exponent.
Solving can be done in the following manner.
[tex]1.~ (xy^2)^2 = x^2(y^{2\times 2}) = x^2y^4\\\\2.~ x^3\times x^3 = x^{3+3} = x^6\\\\3.~ 3y^{-2} = 3\displaystyle\frac{1}{y^2} = \frac{3}{y^2}\\\\4.~ 2(x^2)^3 = 2(x^{2\times 3}) = 2(x^6)=2x^6\\\\5.~ -x^2(-x^3) = x^{2+3} = x^5[/tex]
Expression 4 and 5 were wrongly evaluated.
