Answer :

To solve the equation [tex]\( y^4 = 169 \)[/tex], you need to find the value of [tex]\( y \)[/tex] that makes the equation true.

Here are the steps to solve it:

1. Understand the equation: You have the equation [tex]\( y^4 = 169 \)[/tex]. This means any value of [tex]\( y \)[/tex] raised to the fourth power will equal 169.

2. Find the fourth root: To solve for [tex]\( y \)[/tex], you need to take the fourth root of both sides of the equation.

3. Consider both positive and negative roots: While taking the root, remember that both a positive and a negative number raised to an even power (like 4) will result in a positive number. Therefore, you should consider both:

[tex]\[
y = \sqrt[4]{169} \quad \text{and} \quad y = -\sqrt[4]{169}
\][/tex]

4. Calculate the fourth root of 169: After calculating, you find that [tex]\( \sqrt[4]{169} \approx 3.605551275463989 \)[/tex].

5. Write the solutions: There are two solutions for [tex]\( y \)[/tex]:

[tex]\[
y \approx 3.605551275463989
\][/tex]

and

[tex]\[
y \approx -3.605551275463989
\][/tex]

So, the solutions to the equation [tex]\( y^4 = 169 \)[/tex] are approximately [tex]\( y = 3.605551275463989 \)[/tex] and [tex]\( y = -3.605551275463989 \)[/tex].

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Rewritten by : Barada