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Popular >

simplify (8x^3y^6)^{1/2}

Solution

simplify

(8 x^{3} y^{6})^{\frac{1}{2}}

Solution

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

Solution steps

(8 x^{3} y^{6})^{\frac{1}{2}}

Apply exponent rule:

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

(8 x^{3} y^{6})^{\frac{1}{2}} = 8^{\frac{1}{2}} (x^{3})^{\frac{1}{2}} (y^{6})^{\frac{1}{2}}

= 8^{\frac{1}{2}} (x^{3})^{\frac{1}{2}} (y^{6})^{\frac{1}{2}}

8^{\frac{1}{2}} = 2 \cdot 2^{\frac{1}{2}}

= 2 \cdot 2^{\frac{1}{2}} (x^{3})^{\frac{1}{2}} (y^{6})^{\frac{1}{2}}

Simplify

(x^{3})^{\frac{1}{2}} : x^{\frac{3}{2}}

= 2 \cdot 2^{\frac{1}{2}} x^{\frac{3}{2}} (y^{6})^{\frac{1}{2}}

Simplify

(y^{6})^{\frac{1}{2}} : y^{3}

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

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

= 2^{\frac{3}{2}} x^{\frac{3}{2}} y^{3}

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

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

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Frequently Asked Questions (FAQ)

What is (8x^3y^6)^{1/2} ?
The solution to (8x^3y^6)^{1/2} is 2*2^{1/2}y^3x^{3/2}