Problem Solving

a^99! that's mean a^1*a^2*....*a^99 or [(a^1)^2.....]^99???


The question confuse me a lot! thaks!

in my opinion it means a^(1*2*3*....99)

no, it's when you multiply a 99! times --> a*a*a*a*a*a*a*a*... a (total 99! times)
can be further rewritten as (a^98!)^99 OR (a^97!)^(98*99)

327356719 wrote:a^99! that's mean a^1*a^2*....*a^99 or [(a^1)^2.....]^99???


The question confuse me a lot! thaks!

Night reader wrote:no, it's when you multiply a 99! times --> a*a*a*a*a*a*a*a*... a (total 99! times)
can be further rewritten as (a^98!)^99 OR (a^97!)^(98*99)

327356719 wrote:a^99! that's mean a^1*a^2*....*a^99 or [(a^1)^2.....]^99???


The question confuse me a lot! thaks!

Could actually mean either way, depending on whether the '!' sign is part of the exponent or not. If the ! sign is in the exponent superscript, then Night reader's interpretation is correct: we first deal with the exponent (i.e. figure out what is 99!), then multiply a by itself that huge number of times.
If the '!' sign is not part of the exponent, then we first figure out the power a^99, then make THAT number factorial.