Question

What's 49 to the power of 1/2?

Answer 1

Basically, questions like these would be opposite; find the number that when multiplied by each other equals 49.

Just find the square root of 49.
$\sqrt49=7$

So, $49^ \frac{1}{2} =7$

Our answer is 7.

Answer 2

7

Further explanation

We certainly already know that 49 = 7².

To be able to answer this question, let us use one of the following exponent properties.

$\boxed{\boxed{ \ (x^a)^b = x^{ab} \ }}$

$\boxed{ \ = (49)^{\frac{1}{2}} \ }$

$\boxed{ \ = (7^2)^{\frac{1}{2}} \ }$

$\boxed{ \ = 7^{2 \times \frac{1}{2}} \ }$

$\boxed{ \ = 7^1 \ }$

Thus 49 to the power of ¹/₂ equals 7.

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Now we relate rational exponents with the root form.

In general,

$\boxed{\boxed{ \ x^{\frac{m}{n}} \rightleftharpoons \sqrt[n]{x^m} \ }}.$

Especially for $\boxed{ \ x^{\frac{1}{2}} \ }$ will be $\boxed{ \ \sqrt{x} \ }$

Based on the above properties, 49 to the power ¹/₂ can be written as,

$\boxed{ \ (49)^{\frac{1}{2}} \ } \rightarrow \boxed{ \ \sqrt{49} \ }$

We state it as 'the square root of 49'.

Thus the result is $\boxed{\boxed{\sqrt{49} = 7 \ }}.$

Another example:

What's 100 to the power of ¹/₂ ? The answer is $\boxed{ \ \sqrt{100} = 10 \ }$

Learn more

1. Expression of a sum of cubes brainly.com/question/3638399
2. About complex numbers brainly.com/question/1658190
3. The expression value of the imaginary unit multiplication brainly.com/question/3189119

Keywords: 49 to the power of ¹/₂, 7, the exponent properties, the root form, the square root of 49, the power, rational exponents