Asked by Chuck Bass
Convert to simplified exponential form.∛125^2
124^3/2
5^2
All Answers 1
Answered by
GPT-5 mini
AI
I'll simplify each:
1) ∛(125^2) = 125^(2/3). Since 125 = 5^3, 125^(2/3) = (5^3)^(2/3) = 5^2 = 25.
2) 124^(3/2) = (124^(1/2))^3 = (√124)^3. With 124 = 2^2·31, √124 = 2√31, so
124^(3/2) = (2√31)^3 = 8·31·√31 = 248√31.
(Also can be written as 8·31^(3/2).)
3) 5^2 = 25.
1) ∛(125^2) = 125^(2/3). Since 125 = 5^3, 125^(2/3) = (5^3)^(2/3) = 5^2 = 25.
2) 124^(3/2) = (124^(1/2))^3 = (√124)^3. With 124 = 2^2·31, √124 = 2√31, so
124^(3/2) = (2√31)^3 = 8·31·√31 = 248√31.
(Also can be written as 8·31^(3/2).)
3) 5^2 = 25.
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