Questions: Simplify. √(y^17)

Solution Steps

To simplify the radical expression \(\sqrt{y^{17}}\), we can use the property of exponents that \(\sqrt{a^b} = a^{b/2}\). This means we can rewrite the expression inside the square root as an exponent divided by 2.

We start with the expression \( \sqrt{y^{17}} \). To simplify this, we can use the property of exponents that states \( \sqrt{a^b} = a^{\frac{b}{2}} \).

Applying this property, we rewrite the expression as: \[ \sqrt{y^{17}} = y^{\frac{17}{2}} \]

The exponent \( \frac{17}{2} \) can be expressed as \( 8 + \frac{1}{2} \), which allows us to further simplify: \[ y^{\frac{17}{2}} = y^8 \cdot y^{\frac{1}{2}} = y^8 \sqrt{y} \]

Final Answer