I'm stuck on this I got square root 4096^-1/6 I don't know what to do next
(Square root 16^3) ^-1/6
(Square root 16^3) ^-1/6
(√(16^3) )^(-1/6)
= 16^( (1/2)(3)(-1/6) )
= 16^(-3/12)
= 16^(-1/4)
= 1/16^(1/4)
= 1/2 or .5
or your way:
4096^(-1/6)
= .5 , using my calculator
Is there any other way to solve this?
Here is another slightly different way[16^(3/2)]^-1/6
(4^3)^-1/6
4^-1/2
1/4^(1/2)
1/2
.5
To simplify the expression square root of 4096 raised to the power of -1/6, you can follow these steps:
Step 1: Simplify the innermost part:
The square root of 4096 is equal to 64 because 64 * 64 = 4096.
So, the expression becomes (64)^-1/6.
Step 2: Apply the power rule:
To raise a number to a negative exponent, you take the reciprocal of the number and apply the positive exponent.
Therefore, we can rewrite (64)^-1/6 as 1/(64)^1/6.
Step 3: Simplify the expression:
To simplify (64)^1/6, we need to find the sixth root of 64. A sixth root of a number is a number that, when raised to the power of six, equals the original number.
The sixth root of 64 is 2 because 2 * 2 * 2 * 2 * 2 * 2 = 64.
So, the expression becomes 1/2.
Therefore, the answer to square root of 4096 raised to the power of -1/6 is 1/2 or 0.5.