What is (45x^4*y^{17})^{1/2} ?

The solution to (45x^4*y^{17})^{1/2} is 3*5^{1/2}x^2y^{17/2}

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simplify (45x^4*y^{17})^{1/2}

simplify

(45 x^{4} \cdot y^{17})^{\frac{1}{2}}

3 \cdot 5^{\frac{1}{2}} x^{2} y^{\frac{17}{2}}

Solution steps

(45 x^{4} y^{17})^{\frac{1}{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(45 x^{4} y^{17})^{\frac{1}{2}} = 4 5^{\frac{1}{2}} (x^{4})^{\frac{1}{2}} (y^{17})^{\frac{1}{2}}

= 4 5^{\frac{1}{2}} (x^{4})^{\frac{1}{2}} (y^{17})^{\frac{1}{2}}

4 5^{\frac{1}{2}} = 3 \cdot 5^{\frac{1}{2}}

= 3 \cdot 5^{\frac{1}{2}} (x^{4})^{\frac{1}{2}} (y^{17})^{\frac{1}{2}}

Simplify

(x^{4})^{\frac{1}{2}} : x^{2}

= 3 \cdot 5^{\frac{1}{2}} x^{2} (y^{17})^{\frac{1}{2}}

Simplify

(y^{17})^{\frac{1}{2}} : y^{\frac{17}{2}}

= 3 \cdot 5^{\frac{1}{2}} x^{2} y^{\frac{17}{2}}

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What is (45x^4*y^{17})^{1/2} ?
The solution to (45x^4*y^{17})^{1/2} is 3*5^{1/2}x^2y^{17/2}