Question

PLEASE BRILLIANT
i need help asap

Answer 1

p = 6, q = - 1

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