How does $\frac{21x^3}{x^{1/2}}$ simplify to $21x^{5/2}$

Question

Need clarification on why the fraction $\frac{21x^3}{x^{1/2}}$ simplifies to $21x^{5/2}$. Any help would be appreciated.

Thanks

Answer 1

Using the properties of exponents , a$^b$ .a$^c$ = a$^{b+c}$ and $\frac{1}{a^b}$= a$^{-b}$

Your question beomces $\frac{21x^3}{x^{1/2}}$ = 21.x$^{3-{1/2}}$ = 21x$^{\frac{6-1}{2}}$ = 21x$^{5/2}$.

Answer 2

When you divide $x^3$ by $x^{1/2}$ you need to subtract the exponents.

Note that $$ 3-1/2 = 6/2 - 1/2 = 5/2$$

That is why you have $x^{5/2}$ in your answer.