What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5)

Question

What is the value of  5^{\frac{1}{5}} * 5^{\frac{2}{5}} * 5^{\frac{3}{5}} * 5^{\frac{4}{5}}  ?

A.  \sqrt{5} 
B. 5
C.  5\sqrt{5} 
D. 25
E.  25\sqrt{5}

soumanag · Answer

Apply this formula:  X^a * X^b = X^(a+b)

here: expression comes to 5^1/5 + 2/5 + 3/5 + 4/5 = 5 ^ 10/5 =  5^2  = 25.

Bunuel · Answer

Operations involving the same bases:

Keep the base, add or subtract the exponent (add for multiplication, subtract for division)
 a^n*a^m=a^{n+m}

\frac{a^n}{a^m}=a^{n-m}

So,  5^{\frac{1}{5}}*5^{\frac{2}{5}}*5^{\frac{3}{5}}*5^{\frac{4}{5}}=5^{\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}}=5^{\frac{10}{5}}=5^2=25 .

Hope it helps.

greatchap · Answer

Thanks. I got it. It just slipped initially. I need to add the powers.

sagiyer · Answer

When the base is the same, just add the powers

SO, in this case, 5^ (1/5+2/5+3/5+4/5) = 5^2 = 25

unceldolan · Answer

Can someone add answer choices so we can use the timer? would be great!

Bunuel · Answer

Done. Thank you for the suggestion.

Abhishek009 · Answer

5^{\frac{1}{5}} * 5^{\frac{2}{5}} * 5^{\frac{3}{5}} * 5^{\frac{4}{5}}

Or,  5^{\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}}

Or,  5^{\frac{1+2+3+4}{5}}

Or,  5^{\frac{10}{5}}

Or,  5^2 = 25 , Answer must be (D)

bumpbot · Answer

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What is the value of 5^(1/5)5^(2/5)5^(3/5)*5^(4/5)

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