Answer:
[tex]\frac{1}{36}[/tex]
Step-by-step explanation:
Evaluating the numerator and denominator before evaluating
Using the rule of exponents
[tex]a^{-n}[/tex] ⇔ [tex]\frac{1}{a^{n} }[/tex], [tex]a^{0}[/tex] = 1
Thus
[tex]x^{-2}[/tex]y² ← substitute values into expression
= [tex]3^{-2}[/tex] × 4² = [tex]\frac{1}{9}[/tex] × 16 = [tex]\frac{16}{9}[/tex]
and denominator
[tex]x^{0}[/tex][tex]y^{3}[/tex] = 1 × 4³ = 1 × 64 = 64
Now dividing
[tex]\frac{16}{9}[/tex] ÷ 64
= [tex]\frac{16}{9}[/tex] × [tex]\frac{1}{64}[/tex] ( cancel 16 and 64 )
= [tex]\frac{1}{9(4)}[/tex] = [tex]\frac{1}{36}[/tex]
