What is the value of
$5^{\tfrac{1}{5}} \cdot 5^{\tfrac{2}{5}} \cdot 5^{\tfrac{3}{5}} \cdot 5^{\tfrac{4}{5}}$ ?

Correct answer marked below

5\sqrt{5}

5

5^5\sqrt{5}

25

Correct

25\sqrt{5}

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Explanation

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Comments

ArjunJul 20

thanks, this one was pretty quick once you remember to add the exponents

HarshitaJul 26

yep same here, took me like 15 seconds

KshitizJun 30

wait do you add the exponents or multiply them? i always mix that up when the bases are the same

JulietJul 9

you add them when you're multiplying same base. multiply only happens with a power to a power

KaranAug 31

The fractions 1/5 through 4/5 sum nicely so it simplifies fast. nice easy one

AnmolAug 15

huh i got 5 at first because i forgot to actually sum the numerators properly lol. good reminder to slow down even on easy ones

What this question tests

Your handling of square and higher roots, including simplifying radicals.

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.

What is the value of515⋅525⋅535⋅5455^{\tfrac{1}{5}} \cdot 5^{\tfrac{2}{5}} \cdot 5^{\tfrac{3}{5}} \cdot 5^{\tfrac{4}{5}}551​⋅552​⋅553​⋅554​?