please solve this question and tell correct ans ill mark you brailiest
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Step-by-step explanation:
Given :
(xᵐ/xⁿ)ᵐ⁺ⁿ. (xⁿ/xˡ)ⁿ⁺ˡ.(xˡ/xᵐ)ˡ⁺ᵐ
To find :
The simplified value of the given expression.
Solution :
(xᵐ/xⁿ) can be written as,
=> (xᵐ⁻ⁿ)
Since,
(aᵐ/aⁿ) = (aᵐ⁻ⁿ)
Similarly (xⁿ/xˡ)ⁿ⁺ˡ and (xˡ/xᵐ)ˡ⁺ᵐ
=> (xᵐ⁻ⁿ)ᵐ⁺ⁿ.(xⁿ⁻ˡ)ⁿ⁺ˡ.(xˡ⁻ᵐ)ˡ⁺ᵐ
Now,
=> Bases are same, add the power.
=> (x)ᵐ⁻ⁿ + ᵐ⁺ⁿ + ⁿ⁻ˡ + ⁿ⁺ˡ + ˡ⁻ᵐ + ˡ⁺ᵐ
=> (x)⁰ = 1
∴ 1 is the simplified value of (xᵐ/xⁿ)ᵐ⁺ⁿ. (xⁿ/xˡ)ⁿ⁺ˡ.(xˡ/xᵐ)ˡ⁺ᵐ.
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