# How do you simplify (3^(1/2))^2?

Mar 19, 2018

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

#### Explanation:

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

Mar 19, 2018

${3}^{1} = 3$

#### Explanation:

Rules of exponents says
${\left({a}^{m}\right)}^{n} = {a}^{m n}$

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

So
${\left({3}^{\frac{1}{2}}\right)}^{2} = {3}^{\left(\frac{1}{2}\right) \cdot 2}$

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

${3}^{1} = 3$

Mar 19, 2018

$3$

#### Explanation:

${3}^{\left(\frac{1}{2}\right) 2}$

${3}^{\frac{2}{2}} \to \text{multiplying the exponents}$

${3}^{1}$

$3$