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What is the value of the expression below?

[tex]\[ \left\{64^3\right\}^{1 / 6} \][/tex]

A. 32
B. 64
C. 8
D. 4


Sagot :

To find the value of the expression [tex]\(\left\{64^3\right\}^{1 / 6}\)[/tex], we can simplify it step by step using properties of exponents.

First, let's rewrite the given expression:
[tex]\[ \left(64^3\right)^{1/6} \][/tex]

Using the property of exponents [tex]\((a^m)^n = a^{m \cdot n}\)[/tex], we can combine the exponents:
[tex]\[ (64^3)^{1/6} = 64^{3 \cdot \frac{1}{6}} \][/tex]

Now, multiply the exponents:
[tex]\[ 64^{3 \cdot \frac{1}{6}} = 64^{1/2} \][/tex]

The expression [tex]\(64^{1/2}\)[/tex] represents the square root of 64:
[tex]\[ 64^{1/2} = \sqrt{64} \][/tex]

The square root of 64 is:
[tex]\[ \sqrt{64} = 8 \][/tex]

Therefore, the value of the expression [tex]\((64^3)^{1/6}\)[/tex] is:
[tex]\[ 8 \][/tex]

So, the correct answer is [tex]\(C. 8\)[/tex].