2nd Power

Algebra Level 1

What is the value of

$2^{-100}\cdot2^{-99}\cdot2^{-98}\cdots2^{-1}\cdot2^{0}\cdot2^{1}\cdots 2^{98}\cdot2^{99}\cdot2^{100} = \quad?$

1

2

0

2^{100}

2 solutions

Mahdi Raza
Feb 23, 2020

$\begin{aligned} \text{Expression } &= 2^{-100}\cdot2^{-99}\cdot2^{-98}\cdots2^{-1}\cdot2^{0}\cdot2^{1}\cdots2^{98}\cdot2^{99}\cdot2^{100} \\ &= \cancel{\frac{1}{2^{100}}\cdot\frac{1}{2^{99}} \cdot \frac{1}{2^{98}} \cdots \frac{1}{2^{1}}}\cdot 2^{0} \cdot \cancel{2^{1}\cdots2^{98}\cdot2^{99}\cdot2^{100}} \\ &= 2^0 \\ &= \boxed{1} \end{aligned}$

Quite easy.

Nikola Alfredi - 1 year, 3 months ago

Ya, it is just an elementary problem for exponents

Mahdi Raza - 1 year, 3 months ago

Do not click , but if you do then see the solution.

Nikola Alfredi - 1 year, 3 months ago

very surprised and happy to find a fifteen year old Indian here! you're quite brilliant! all the best for your future!

Anu K - 1 year, 3 months ago

Thank you so much Anu :), you too are just 16 and have just began your journey on brilliant I think. You will explore lots of problems here by geniuses around the globe. All the best to you as well!

Mahdi Raza - 1 year, 3 months ago

Yes, indeed, I'm quite new here. Was quite upset about finding this wonderful place at such a critical time of the year. Nonetheless, I'm quite happy to see such amazing people and get a chance to work my brain with such intriguing challenges!

Thanks for the well wishes, Mahdi. Have a great day!

Anu K - 1 year, 3 months ago

@Mahdi Raza - I think there's a error in 2nd line, shouldn't it be $\frac{1}{2^{100}}$ instead of $\frac{1}{2^{-100}}$ . For all of the fractions that have negative power of 2 as denominator? Please correct me if im wrong!

A Former Brilliant Member - 11 months ago

Oopsies, you are absolutely right. Thanks for pointing it out!!

Mahdi Raza - 11 months ago

Joshua Olayanju
May 24, 2020

All the negative exponents will eliminate the positive ones leaving 2^0 hence, equaling 1

2nd Power

2 solutions

@Mahdi Raza - I think there's a error in 2nd line, shouldn't it be 1 2 100 \frac{1}{2^{100}} 2 1 0 0 1 ​ instead of 1 2 − 100 \frac{1}{2^{-100}} 2 − 1 0 0 1 ​ . For all of the fractions that have negative power of 2 as denominator? Please correct me if im wrong!

0 pending reports

@Mahdi Raza - I think there's a error in 2nd line, shouldn't it be $\frac{1}{2^{100}}$ instead of $\frac{1}{2^{-100}}$ . For all of the fractions that have negative power of 2 as denominator? Please correct me if im wrong!