Question

simplify y to the 1/3 ÷ y to the -3/2 y to the 1/2

Answer 1

$\frac{y^\frac{1}{3}}{y^\frac{-3}{2}y^\frac{1}{2}}$

The rule of exponent says , when two terms with same base are in multiplication , the exponents gets added.

for example

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

and when two terms are in division with same base , the exponents are subtracted

for example

a^m /a^n = a^(m-n)

So applying these rules

we get

$\frac{y^\frac{1}{3}}{y^{\frac{-3}{2}+\frac{1}{2}} }$

= $\frac{y^\frac{1}{3}}{y^{\frac{-2}{2}}}$

=$\frac{y^\frac{1}{3}}{y^{-1}}$

=$y^{\frac{1}{3}-1}$

=$y^\frac{-2}{3}$

=$\frac{1}{y^{\frac{2}{3}}}$