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

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

• A. α^n β^n + γ^n δ^n
• B. (αβγδ)^n
• C. α^n β^n γ^n δ
• D. α^n β^n γ^n / δ^n

Answer: (B)

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.

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.