Question

question express the following fraction in simplest form using only positive exponents. \\(\frac{3y^4}{5(y^2)^2}\\)

Explanation:

Step1: Simplify denominator exponent

Use power rule: $(a^m)^n=a^{m \cdot n}$
$\frac{3y^4}{5y^{2 \cdot 2}} = \frac{3y^4}{5y^4}$

Step2: Cancel like variable terms

Apply quotient rule: $\frac{a^m}{a^n}=a^{m-n}$
$\frac{3}{5} \cdot y^{4-4} = \frac{3}{5} \cdot y^0$

Step3: Simplify zero exponent

Use $a^0=1$ (where $a
eq 0$)
$\frac{3}{5} \cdot 1 = \frac{3}{5}$

Answer:

$\frac{3}{5}$