Question

find ⁿ if (-2/3)-¹³×(3/-2)⁸=(-2/3)-²ⁿ+¹​

Answer 1

Answer:

The value of 'n' is 11

Step-by-step explanation:

Given that,

(-2/3)⁻¹³ × (3/-2)⁸ = (-2/3)⁻²ⁿ⁺¹

(∵ a⁻ˣ can be written as reciprocal of aˣ i.e; a⁻ˣ = 1/a⁻⁽⁻ˣ⁾ = 1/aˣ )

⇒(-3/2)¹³ × (-3/2)⁸ = (-3/2)⁻⁽⁻²ⁿ⁺¹⁾

(∵ aᵇ × aˣ = a⁽ᵇ⁺ˣ⁾ )

⇒ (-3/2)¹³⁺⁸ = (-3/2)⁻⁽⁻²ⁿ⁺¹⁾

Compare both LHS & RHS,

As the bases are equal their exponential powers will also be equal

⇒ 13 + 8 = -(-2n+1)

(∵ '-' × '-' = '+' & '-' × '+' = '-')

⇒ 21 = 2n - 1

⇒ 2n = 21+1

⇒ 2n = 22

⇒ n = 11

∴ The value of 'n' is 11

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