Evaluate:
16^-3/4
16^(-3/4) = 1/(16^3/4)
= 1/(4th root 16)^3
= 1/(2)^3
= 1/8
To evaluate 16^(-3/4), we can follow these steps:
Step 1: Rewrite the expression with a positive exponent by taking the reciprocal of the base.
16^(-3/4) is equivalent to 1/16^(3/4).
Step 2: Evaluate the base raised to the fractional exponent.
To find the value of 16^(3/4), we need to understand what a fractional exponent means. In this case, a fractional exponent represents the fourth root (denominator) of the base raised to the power of the numerator.
The fourth root of 16 can be found by asking "What number, when raised to the power of 4, gives us 16?" The answer is 2, as 2^4 = 16.
Thus, 16^(3/4) equals (the fourth root of 16)^3, which equals 2^3, which is 8.
Therefore, 16^(-3/4) is equal to 1/8.
To summarize:
16^(-3/4) = 1/16^(3/4) = 1/(4th root of 16)^3 = 1/8.