To simplify the expression [tex]\( 4y^{12} \cdot y^8 \)[/tex], follow these steps:
1. Identify the properties of exponents:
- When you multiply expressions that have the same base, you can add the exponents. This is known as the product of powers property: [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex].
2. Apply the property to combine the terms with the same base [tex]\(y\)[/tex]:
- In [tex]\( 4y^{12} \cdot y^8 \)[/tex], the base [tex]\( y \)[/tex] is common in both terms.
- Add the exponents: [tex]\( 12 + 8 = 20 \)[/tex].
3. Simplify the expression:
- This gives us [tex]\( y^{20} \)[/tex].
4. Combine the coefficient with the simplified exponent:
- The coefficient [tex]\(4\)[/tex] remains unchanged, as it is not affected by the properties of exponents.
Thus, the simplified expression is:
[tex]\[ 4y^{20} \][/tex]
