A Level Further Mathematics Core Pure Practice Test

Which expression equals α^n β^n γ^n δ^n?

α^n β^n + γ^n δ^n (αβγδ)^n α^n β^n γ^n δ α^n β^n γ^n / δ^n

Correct Answer:

(αβγδ)^n

Explanation:

Raising a product to a power distributes the power to each factor: (αβγδ)^n = α^n β^n γ^n δ^n. So the expression with α^n β^n γ^n δ^n is exactly the nth power of the product αβγδ. The other forms don’t match in general: a sum α^n β^n + γ^n δ^n is not a single product and would not simplify to α^n β^n γ^n δ^n; α^n β^n γ^n δ has the δ exponent only 1, not n; and α^n β^n γ^n / δ^n is α^n β^n γ^n δ^{-n}, which puts δ with exponent -n.

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