Question

1. what does \\(\sqrt{x^4}\\) simplify to?

\\(\bigcirc\\) a. \\(2x\\)
\\(\bigcirc\\) b. \\(x^{\frac{1}{2}}\\)
\\(\bigcirc\\) c. \\(x^2\\)
\\(\bigcirc\\) d. \\(x^4\\)

Explanation:

Step1: Recall the property of square roots and exponents

The square root of a number \( y \) can be written as \( y^{\frac{1}{2}} \). So, \( \sqrt{x^4}=(x^4)^{\frac{1}{2}} \).

Step2: Apply the exponent rule \((a^m)^n = a^{m\times n}\)

For \( (x^4)^{\frac{1}{2}} \), we multiply the exponents \( 4 \) and \( \frac{1}{2} \). So, \( 4\times\frac{1}{2} = 2 \). Thus, \( (x^4)^{\frac{1}{2}}=x^{2} \).

Answer:

c. \( x^2 \)