SOLUTION: without using a calculator simplify each of the following a) (27x^3/64a^-3)^-2/3 b) 2^n+1/(2^n)^n-1 / 4^n+1/(2^n-1)^n+1

Write 27 as 3³ and 64 as 4³



Remove the parentheses by multiplying each exponent inside the
parentheses by the  exponent outside the parentheses:



Move all the factors with negative exponents from numerator to
denominator -- and from denominator to numerator, making them 
positive.  Leave the a² in the denominator because it already 
has a positive exponent.



Finally write 4² as 16 and 3² as 9



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Change the 4 to 2²



Remove all the parentheses by multiplying inner and outer
exponents of 2:



Invert the second fraction and change the division to 
multiplication:

  

Subtract exponents of 2 in each fraction:



Remove the parentheses in the exponents:



Combine like terms in the exponents:



Add exponents of 2:












Edwin