Do brackets make any difference?
( 5 4 3 ) 2 1 × 5 ( 4 3 ) 2 1 = 5 b ; b = ?
The answer is 4224.
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2 solutions
The answer was nicely symmetric.
There is still a lack of parenthesis that make the problem ambiguous (what is 5 4 3 ?) and I suppose this is why we had multiple answer attempts. ( 5 4 ) 3 = 5 ( 4 3 )
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Actually, no ambiguous expression there. It is common to find expressions like these, with several levels of exponentiation. Given that operation is not conmutative, you have to assume (and that's the common agreement for this notation) that 5 4 3 means 5 ( 4 3 ) . And, of course, as you point ( 5 4 ) 3 = 5 3 ⋅ 4 = 5 1 2 = 5 ( 4 3 ) = 5 2 6 = 5 6 4
Tower rule.
the 2nd one , its 5 ^ 64 ^ 2 ^ 1 after opening the bracket , i dont see the reason for u to solve 64 ^ 2 before 5 ^ 64
Alternatively, (5^64)^2 x 5^(64^2) = 5^64 x 5^64 x 5^(64x64) = 5^(64+64+(64x64)) = 5^(66x64) = 5^b. So b = 66x64 = 4224.
\(\large\begin{array}{} (5^{4^{3}})^{2^{1}} \times 5^{(4^{3})^{2^{1}}} &= (5^{64})^{2} \times 5^{(64^{2})} \\ &= 5^{128} \times 5^{4096} \\ &= 5^{4224} \\ \boxed{b = 4224}\end{array}\)