To simplify the expression [tex]\( x^8 \cdot x^2 \)[/tex] using the laws of exponents, we can follow these steps:
1. Identify the bases and exponents:
- The base in both terms is [tex]\( x \)[/tex].
- The exponents are 8 and 2 respectively.
2. Apply the product rule of exponents:
- The product rule states that when multiplying two expressions that have the same base, you add the exponents. Mathematically, this rule is expressed as:
[tex]\[
x^a \cdot x^b = x^{a+b}
\][/tex]
where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the exponents and the base [tex]\( x \)[/tex] is common.
3. Add the exponents:
- For [tex]\( x^8 \cdot x^2 \)[/tex], we add the exponents 8 and 2.
[tex]\[
8 + 2 = 10
\][/tex]
4. Write the simplified expression:
- After adding the exponents, the expression [tex]\( x^8 \cdot x^2 \)[/tex] simplifies to:
[tex]\[
x^{10}
\][/tex]
Thus, the simplified expression is:
[tex]\[
x^{10}
\][/tex]
