What is [tex]49[/tex] to the power of [tex]\frac{1}{2}[/tex]?

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 .
( x a ) b = x ab ​ ​
= ( 49 ) 2 1 ​ ​
= ( 7 2 ) 2 1 ​ ​
= 7 2 × 2 1 ​ ​
= 7 1 ​
Thus 49 to the power of ¹/₂ equals 7.

Now we relate rational exponents with the root form.
In general,
x n m ​ ⇌ n x m ​ ​ ​ .
Especially for x 2 1 ​ ​ will be x ​ ​
Based on the above properties, 49 to the power ¹/₂ can be written as,
( 49 ) 2 1 ​ ​ → 49 ​ ​
We state it as 'the square root of 49'.
Thus the result is 49 ​ = 7 ​ ​ .
**Another example: **
What's 100 to the power of ¹/₂ ? The answer is 100 ​ = 10 ​
Learn more

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

Answered by BladeRunner212 | 2024-06-12

By the use of ** exponent properties ** we get, 7 is 49 to the** power **of 1/2.
Let us use one of the following** exponent properties.**
(xᵃ)ᵇ = xᵃᵇ
4 9 1/2 = ( 7 2 ) 1/2 )
2 * 1/2 = 2/2
= 1
7¹ = 7.
Therefore, 49 to the power of 1/2 is equal to 7.
Learn more about exponent here:
https://brainly.com/question/5497425
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Answered by bhawsarsakshi4 | 2024-06-17

Raising 49 to the power of 2 1 ​ is the same as finding the square root of 49 . The square root of 49 is 7 . Therefore, 4 9 2 1 ​ = 7 .
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Answered by BladeRunner212 | 2024-09-30