Simplify the expression below: [tex]\left(8^2\right)^6[/tex]

A. [tex]8^8[/tex]
B. [tex]8^4[/tex]
C. [tex]8^{12}[/tex]
D. [tex]8^3[/tex]



Answer :

To simplify the expression \(\left(8^2\right)^6\), we need to use the properties of exponents. Specifically, the property that states \(\left(a^m\right)^n = a^{m \cdot n}\).

Here’s the step-by-step solution:

1. Identify the base and the exponents in the given expression:
- The base is \(8\).
- The inner exponent is \(2\).
- The outer exponent is \(6\).

2. Apply the exponent multiplication rule \(\left(a^m\right)^n = a^{m \cdot n}\):
[tex]\[ \left(8^2\right)^6 = 8^{2 \cdot 6} \][/tex]

3. Multiply the exponents:
[tex]\[ 2 \cdot 6 = 12 \][/tex]

4. Simplify the expression:
[tex]\[ 8^{2 \cdot 6} = 8^{12} \][/tex]

Therefore, the simplified form of \(\left(8^2\right)^6\) is \(8^{12}\).

Thus, the correct answer is:
C. [tex]\(8^{12}\)[/tex]