Question

simplify \\(sqrt{16y^{16}}\\). \\(\bigcirc\\ 4y^4\\) \\(\bigcirc\\ 4y^8\\) \\(\bigcirc\\ 8y^4\\) \\(\bigcirc\\ 8y^8\\)

Explanation:

Step1: Simplify the square root of 16

The square root of 16 is 4, since \( \sqrt{16} = 4 \).

Step2: Simplify the square root of \( y^{16} \)

Using the property of exponents \( \sqrt{a^m} = a^{\frac{m}{2}} \), for \( a = y \) and \( m = 16 \), we have \( \sqrt{y^{16}} = y^{\frac{16}{2}} = y^8 \).

Step3: Multiply the results

Multiply the results from Step 1 and Step 2: \( 4 \times y^8 = 4y^8 \).

Answer:

\( 4y^8 \) (which corresponds to the option "4\( y^8 \)")