7
We certainly already know that 49 = 7².
To be able to answer this question, let us use one of the following exponent properties.
[tex]\boxed{\boxed{ \ (x^a)^b = x^{ab} \ }}[/tex]
[tex]\boxed{ \ = (49)^{\frac{1}{2}} \ }[/tex]
[tex]\boxed{ \ = (7^2)^{\frac{1}{2}} \ }[/tex]
[tex]\boxed{ \ = 7^{2 \times \frac{1}{2}} \ }[/tex]
[tex]\boxed{ \ = 7^1 \ }[/tex]
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,
[tex]\boxed{\boxed{ \ x^{\frac{m}{n}} \rightleftharpoons \sqrt[n]{x^m} \ }}.[/tex]
Especially for [tex]\boxed{ \ x^{\frac{1}{2}} \ }[/tex] will be [tex]\boxed{ \ \sqrt{x} \ }[/tex]
Based on the above properties, 49 to the power ¹/₂ can be written as,
[tex]\boxed{ \ (49)^{\frac{1}{2}} \ } \rightarrow \boxed{ \ \sqrt{49} \ }[/tex]
We state it as 'the square root of 49'.
Thus the result is [tex]\boxed{\boxed{\sqrt{49} = 7 \ }}.[/tex]
Another example:
What's 100 to the power of ¹/₂ ? The answer is [tex]\boxed{ \ \sqrt{100} = 10 \ }[/tex]
Keywords: 49 to the power of ¹/₂, 7, the exponent properties, the root form, the square root of 49, the power, rational exponents
