How do you rewrite with fractional exponents for $\sqrt{\frac{4 m n}{a^{2} b^{2}}}$ $sqrt((4mn)/(a^2b^2))$ ?

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How do you rewrite with fractional exponents for $\sqrt{\frac{4 m n}{a^{2} b^{2}}}$ $sqrt((4mn)/(a^2b^2))$ ?

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Answer 1 · 2018-03-06T13:08:17

$\frac{2 {(m n)}^{\frac{1}{2}}}{a b}$ $(2(mn)^(1/2))/(ab)$

Explanation:

Since we say that $\sqrt{x} = x^{\frac{1}{2}}$ $sqrt(x)=x^(1/2)$ , we can write the above as:

$\frac{{(4 m n)}^{\frac{1}{2}}}{{(a^{2} b^{2})}^{\frac{1}{2}}}$ $(4mn)^(1/2)/(a^2b^2)^(1/2)$

Since ${(x y)}^{z} = x^{z} y^{z}$ $(xy)^z=x^zy^z$ , we can write:

$\frac{4^{\frac{1}{2}} m^{\frac{1}{2}} n^{\frac{1}{2}}}{{(a^{2})}^{\frac{1}{2}} {(b^{2})}^{\frac{1}{2}}}$ $(4^(1/2)m^(1/2)n^(1/2))/((a^2)^(1/2)(b^2)^(1/2))$

Some of these cancel out:

$\frac{2 m^{\frac{1}{2}} n^{\frac{1}{2}}}{a b}$ $(2m^(1/2)n^(1/2))/(ab)$ , and to make this look nicer, we can write:

$\frac{2 {(m n)}^{\frac{1}{2}}}{a b}$ $(2(mn)^(1/2))/(ab)$

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How do you rewrite with fractional exponents for $\sqrt{\frac{4 m n}{a^{2} b^{2}}}$ $sqrt((4mn)/(a^2b^2))$ ?

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Explanation:

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How do you rewrite with fractional exponents for sqrt((4mn)/(a^2b^2))√4mna2b2sqrt((4mn)/(a^2b^2))?

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Explanation:

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How do you rewrite with fractional exponents for $\sqrt{\frac{4 m n}{a^{2} b^{2}}}$ $sqrt((4mn)/(a^2b^2))$ ?