the 100th root of 10^10^10
Answers
Answer:
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Step-by-step explanation:
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: Let the required value is x. If we multiply x for 100 times we will get 10(1010).
Form an equation according to this condition and solve the value of x.
Complete step by step answer:
Let the number is x.
Therefore the 100th root of 10(1010) is x.
That means if we multiply x for 100 times we will get 10(1010).
Or we can say if we take x to the power 100 we will get 10(1010). An expression that represents repeated multiplication of the same factor is called a power. Or we can say the power of a number says how many times to use the number in a multiplication.
Hence, x100=10(1010)
From this equation we have to find out the value of x.
Therefore we have,
x100=10(1010)
Now we can take the power of x that is 100 from our left hand side to right hand side,
⇒x=(10(1010))1100⇒x=101010100
We can write 100 as 10 multiplied by 10. Therefore,
⇒x=10101010×10⇒x=101010102⇒x=101010−2⇒x=10108
Therefore, the 100th root of 10(1010) is 10108.
Hence option (b) is correct.
Note: Alternatively we can find out the answer by cross checking the options. Take the options one by one and see if that option to the power 100 is 10(1010) or not.
Like for option (b),
(10108)100=10108×100=10108×102=10108+2=101010
Hence option (b) is correct.
There is a difference between the 100th root of a number and that number to the power 100.
100th root of a number, say x, means x1100.
And x to the power 100 is x100.