How do you simplify ${(3^{\frac{1}{2}})}^{2}$ $(3^(1/2))^2$ ?

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How do you simplify ${(3^{\frac{1}{2}})}^{2}$ $(3^(1/2))^2$ ?

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Answer 1 · 2018-03-19T12:47:38

It would be just 3 (or $3^{1}$ $3^1$ ).

Explanation:

The exponent power rule states the ${(a^{n})}^{m} = a^{n m}$ $(a^n) ^m = a^ (nm)$
Applying this rule to ${(3^{\frac{1}{2}})}^{2}$ $(3^(1/2))^2$ will get us $3^{\frac{1}{2} \cdot 2}$ $3^(1/2 * 2)$ which is $3^{1}$ $3^1$ or just 1.
To verify this answer, we can actually evaluate the exponent. $3^{\frac{1}{2}}$ $3^(1/2)$ is equal to the square root of three. The square of the square root of 3 is just 3.

Answer 2 · 2018-03-19T12:48:35

$3^{1} = 3$ $3^1=3$

Explanation:

Rules of exponents says
${(a^{m})}^{n} = a^{m n}$ $(a^m)^n=a^(mn)$

Where
$a = 3$ $a=3$
$m = \frac{1}{2}$ $m=1/2$
$n = 2$ $n=2$

So
${(3^{\frac{1}{2}})}^{2} = 3^{(\frac{1}{2}) \cdot 2}$ $(3^(1/2))^2=3^((1/2)*2)$

${(3^{\frac{1}{2}})}^{2} = 3^{1}$ $(3^(1/2))^2=3^1$

$3^{1} = 3$ $3^1=3$

Answer 3 · 2018-03-19T12:54:37

$3$ $3$

Explanation:

$3^{(\frac{1}{2}) 2}$ $3^((1/2)2)$

$3^{\frac{2}{2}} \to multiplying the exponents$ $3^(2/2) ->"multiplying the exponents"$

$3^{1}$ $3^1$

$3$ $3$

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