1417×1417 can be represented as ___________.

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Question

14^{\frac{1}{7}} \times 14^{\frac{1}{7}}

can be represented as ___________.

Options:

A . 1417+17

B . (142)17

C . (14×14)17

D . All of the above

Answer: Option D
:
D
For any positive real number '

a

' and integers '

m

' and '

n

', we define
1.

a^{m} \times a^{n} = a^{m + n}

2.

{(a^{m})}^{n} = a^{m n}

3.

(a b)^{m} = a^{m} b^{m}

andif

a = b

, the expression becomes

(a \times a)^{m} = (a^{2})^{m} = a^{2 m}

.
So, using first rule, we have

14^{\frac{1}{7} + \frac{1}{7}} = 14^{\frac{2}{7}}

Now, using secondrule,

(14^{2})^{\frac{1}{7}}

=

14^{\frac{2}{7}}

Finally, using thirdrule,
(

14 \times 14)^{\frac{1}{7}} = 14^{\frac{2}{7}}

Hence, we see that all the three results are same.

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