Situation of chaos ? #2

Algebra Level 2

2 3 2 3 2 0 2 3 = 2 ( 3 2 ) 3 2 0 2 3 \huge \color{#3D99F6}{2^{3^{2^{3^{2^{0^{2^3}}}}}}}=\color{#20A900}{{2^{\left( 3^2 \right)}}^{3^{2^{0^{2^3}}}}}

Which of the options is true about the above equation ?


Join the Brilliant Classes and enjoy the excellence.
False True Ambiguous

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Feathery Studio
May 28, 2015

To simplify exponents, we do each exponent from top to bottom.

On the L.H.S., we can turn the 0 0 and all the exponents after it into a 0 0 . Then we have 2 0 = 1 2^{0} = 1 . So now our L.H.S. expression is 2 3 2 3 2^{3^{2^{3}}} . As for the R.H.S., we'll get rid of brackets first, so our R.H.S. expression is 2 9 3 2 0 2 3 2^{9^{3^{2^{0^{2^{3}}}}}} . We can apply the process done on the L.H.S., so we get 2 9 3 2^{9^{3}} .

L.H.S.: 2 3 2 3 = 2 3 8 = 2 6561 2^{3^{2^{3}}} = 2^{3^{8}} = 2^{6561}

R.H.S.: 2 9 3 = 2 729 2^{9^{3}} = 2^{729}

The two sides are not equal.

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...