To simplify the expression \( 16^{1/4} \), we start by understanding the base, which is \( 16 \).
-
Express 16 in terms of its prime factors: \[ 16 = 2^4 \]
-
Substitute this back into the expression: \[ 16^{1/4} = (2^4)^{1/4} \]
-
Use the power of a power property: According to the property of exponents \( (a^m)^n = a^{m \cdot n} \), we can simplify this further: \[ (2^4)^{1/4} = 2^{4 \cdot \frac{1}{4}} = 2^1 = 2 \]
Thus, \( 16^{1/4} = 2 \).
Summary of Factors to Simplify
The key factors that helped simplify the expression were:
- Recognizing that \( 16 \) can be written as \( 2^4 \).
- Using the power of a power property of exponents to simplify the expression.
Therefore, the simplified result of \( 16^{1/4} \) is \( 2 \).
5 answers