Answer:
p = 6, q = - 1
Step-by-step explanation:
Using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , [tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex]
Given
xy = 32 , tat is
[tex]2^{p}[/tex] × [tex]2^{q}[/tex] = [tex]2^{5}[/tex]
Since the bases on both sides are equal, equate the exponents
p + q = 5 → (1)
Also
2xy² = 32 ( divide both sides by 2 )
xy² = 16 , that is
[tex]2^{p}[/tex] × [tex](2^{q}) ^{2}[/tex] = 16
[tex]2^{p}[/tex] × [tex]2^{2q}[/tex] = [tex]2^{4}[/tex] , then p + 2q = 4 → (2)
Thus
p + q = 5 → (1)
p + 2q = 4 → (2)
Subtract (1) from (2) term by term
q = - 1
Substitute q = - 1 into (1) for corresponding value of p
p - 1 = 5 ( add 1 to both sides )
p = 6
