To simplify the expression \((x^6)(x^2)\), you need to apply the properties of exponents. Here are the detailed steps:
1. Identify the Rule:
When multiplying exponential expressions with the same base, you add the exponents. This is known as the Product of Powers property. Mathematically, this is given by:
[tex]\[
x^a \cdot x^b = x^{a+b}
\][/tex]
2. Apply the Rule:
In the expression \((x^6)(x^2)\), both exponents have the base \(x\).
- The first exponent is \(6\).
- The second exponent is \(2\).
According to the Product of Powers property, you add the exponents together:
[tex]\[
(x^6)(x^2) = x^{6+2}
\][/tex]
3. Simplify the Exponents:
Adding the exponents together:
[tex]\[
6 + 2 = 8
\][/tex]
4. Write the Final Expression:
Therefore, the simplified expression is:
[tex]\[
x^8
\][/tex]
So the correct answer is:
C. [tex]\( x^8 \)[/tex]
