Question

adical expressions
5 100%
√y⁴
simplify

Explanation:

Step1: Recall radical and exponent rules

The square root of a number \( x \) is \( x^{\frac{1}{2}} \), and \((a^m)^n=a^{m\times n}\). For \(\sqrt{y^4}\), we can rewrite the square root as an exponent: \(\sqrt{y^4}=(y^4)^{\frac{1}{2}}\).

Step2: Apply the exponent rule

Using the power - of - a - power rule \((a^m)^n = a^{m\times n}\), where \(a = y\), \(m = 4\), and \(n=\frac{1}{2}\), we have \((y^4)^{\frac{1}{2}}=y^{4\times\frac{1}{2}}\).

Step3: Simplify the exponent

Calculate \(4\times\frac{1}{2}=2\), so \(y^{4\times\frac{1}{2}} = y^{2}\).

Answer:

\(y^{2}\)