Answer :
To find the value of the expression [tex]\(\left\{9^2\right\}^{1 / 4}\)[/tex], let's go through the problem step-by-step.
1. Evaluate [tex]\(9^2\)[/tex]:
[tex]\[ 9^2 = 9 \times 9 = 81. \][/tex]
2. Now substitute the result back into the original expression:
[tex]\[ \left\{9^2\right\}^{1 / 4} = 81^{1 / 4}. \][/tex]
3. Find the fourth root of 81:
[tex]\[ 81^{1 / 4} = \sqrt[4]{81}. \][/tex]
To determine [tex]\(\sqrt[4]{81}\)[/tex], we look for a number which, when raised to the power of 4, equals 81.
Recall:
[tex]\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81. \][/tex]
So,
[tex]\[ \sqrt[4]{81} = 3. \][/tex]
Thus, the value of the expression [tex]\(\left\{9^2\right\}^{1 / 4}\)[/tex] is [tex]\(\boxed{3}\)[/tex]. Hence, the correct answer is B.
1. Evaluate [tex]\(9^2\)[/tex]:
[tex]\[ 9^2 = 9 \times 9 = 81. \][/tex]
2. Now substitute the result back into the original expression:
[tex]\[ \left\{9^2\right\}^{1 / 4} = 81^{1 / 4}. \][/tex]
3. Find the fourth root of 81:
[tex]\[ 81^{1 / 4} = \sqrt[4]{81}. \][/tex]
To determine [tex]\(\sqrt[4]{81}\)[/tex], we look for a number which, when raised to the power of 4, equals 81.
Recall:
[tex]\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81. \][/tex]
So,
[tex]\[ \sqrt[4]{81} = 3. \][/tex]
Thus, the value of the expression [tex]\(\left\{9^2\right\}^{1 / 4}\)[/tex] is [tex]\(\boxed{3}\)[/tex]. Hence, the correct answer is B.
