In the expression $7^4$, which part is the base and which is the exponent?

Consider $x^2\times y^2$. Is the product rule applicable for this expression in order to combine these terms into a single base power? If not, provide an alternative correct simplification.

Simplify $x^{\frac{1}{2}}\cdot x^{\frac{3}{2}}$.

Simplify $2x^3\cdot 5x^{-1}\cdot x^2$, and then evaluate the result for $x=2$.

Simplify: ${(-4)}^2\times {(-4)}^3\times z^5\times z^{-2}$