Question

what does ((49y^{8})^{\frac{1}{2}}) simplify to?
(24.5y^{4})
(7y^{4})
(49y^{8})
(7y^{8})
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Explanation:

Step1: Apply exponent rule \((ab)^n = a^n b^n\)

We can rewrite \((49y^{8})^{\frac{1}{2}}\) as \(49^{\frac{1}{2}} \cdot (y^{8})^{\frac{1}{2}}\) using the exponent rule \((ab)^n = a^n b^n\).

Step2: Simplify \(49^{\frac{1}{2}}\)

We know that \(49^{\frac{1}{2}}=\sqrt{49} = 7\) because the square root of 49 is 7.

Step3: Simplify \((y^{8})^{\frac{1}{2}}\)

Using the exponent rule \((a^m)^n=a^{mn}\), we have \((y^{8})^{\frac{1}{2}}=y^{8\times\frac{1}{2}} = y^{4}\).

Step4: Combine the results

Combining the results from Step 2 and Step 3, we get \(49^{\frac{1}{2}} \cdot (y^{8})^{\frac{1}{2}}=7\times y^{4}=7y^{4}\).

Answer:

B. \(7y^{4}\)