How do you solve 16^-3/4 without a calculator?

16^-3/4
=(16^1/4)^-3
=2^-3
=1/(2^3)
=1/8
.,.,

sixteen^3/4 is the fourthroot of sixteen cubed. what selection, prolonged by way of itself 4 circumstances, equals sixteen? 2 works, via fact 2*2*2*2=sixteen. Now cube that root; 2^3=8, so there is your answer.

first you take the 4th root of 16 which is 2 and then raise it to the -3 power which is 1/8

16= 2x2x2x2 = 2^4

16^(-3/4) = (2^4)^(-3/4) = 2^[4x(-3/4)] = 2^(-3) = 1 / 2^(-3) = 1/8

16 is 2^4 so

(2^4)^-3/4
=2^(-3) ......the 2 4's cancel out each other
=1/2^3
=1/8 .

its so simple....
first remove negative power by reciprocal of 16....
so it becomes 1/16 ^3/4

nw u can see 1^3/4 is 1 only hence numerator is unaffected....
in denomenator 16 can be written as 2^4
hence it becomes 1/2 ^ 3/4*4 which is equal to 1/2 ^ 3

hence answer is 1/8......




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16^-3/4= 1/ (16)^(3/4)
=1 / [(16)^1/4] ^3
1/16^(1/4) is the fourth root of 16 , which is 2, because 2 x 2 x 2 x 2 =16.
2^3 = 8
So, 16^-3/4 =1/ 8

16^(-3/4)
= ±⁴√(1/16^3)
= ±⁴√(1/4096)
= ±⁴√(1/8 * 1/8 * 1/8 * 1/8)
= ±1/8

if you know that 16^(1/4) = 2, then it is easy. If you don't know that you should memorize the first 10 powers of 2.

2^-3 = 1/8, which is your answer

1 / (16^(3/4)

1 / 2³

1 / 8