Question

simplify. assume that no variable equals 0.
$y^7 \cdot y^3 \cdot y^2$
$\bigcirc\\ 3y^{12}$
$\bigcirc\\ y^{42}$
$\bigcirc\\ y^{12}$
$\bigcirc\\ y^2$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying exponential expressions with the same base, we use the rule \( a^m \cdot a^n = a^{m + n} \). Here, the base is \( y \), so we add the exponents.

Step2: Add the exponents

For \( y^7 \cdot y^3 \cdot y^2 \), we add the exponents \( 7 + 3 + 2 \).
\( 7+3 + 2=12 \), so the expression simplifies to \( y^{12} \).

Answer:

\( y^{12} \) (corresponding to the option: \( y^{12} \))