Option D: 81 is the correct answer
Step-by-step explanation:
We have to find a number from the given options whose exponent 1/2 and 1/4 are integers.
First of all we have to exclude first two options with negative numbers as the exponents applied to these numbers will also give a negative number. So option A and option B are excluded
Now
for option C:
32 cannot be written as a square of any number so it is also excluded
We have to check the last option D: 81
Verification:
[tex](81) ^{\frac{1}{2}} = ?\\=(9^2)^{\frac{1}{2}}\\= 9^{(2*\frac{1}{2})}\\= 9[/tex]
[tex](81) ^{\frac{1}{4}} = ?\\=(3^4)^{\frac{1}{4}}\\= 3^{(4*\frac{1}{4})}\\= 3[/tex]
We can see that in cases of both exponents the number is an integer so
Option D: 81 is the correct answer
Keywords: Exponents, integers
Learn more about exponents at:
- brainly.com/question/10666510
- brainly.com/question/10699220
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