Question

PLEASE BRILLIANT i need help asap

Answer 1

Answer:

p = 6, q = - 1

Step-by-step explanation:

Using the rules of exponents

$a^{m}$ × $a^{n}$ = $a^{(m+n)}$ , $(a^{m}) ^{n}$ = $a^{mn}$

Given

xy = 32 , tat is

$2^{p}$ × $2^{q}$ = $2^{5}$

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

$2^{p}$ × $(2^{q}) ^{2}$ = 16

$2^{p}$ × $2^{2q}$ = $2^{4}$ , 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