Question

which expression is equivalent to $-6x^3 \cdot x \cdot y^2 \cdot y^6$?
\bigcirc $-6x^3 y^8$
\bigcirc $-6x^2 y^{12}$
\bigcirc $-6x^4 y^8$
\bigcirc $-6x^4 y^{12}$

Explanation:

Step1: Apply exponent rule for x terms

When multiplying variables with exponents, use \(a^m \cdot a^n = a^{m + n}\). For \(x^3 \cdot x\), \(x = x^1\), so \(x^3 \cdot x^1 = x^{3 + 1}=x^4\).

Step2: Apply exponent rule for y terms

For \(y^2 \cdot y^6\), use the same rule: \(y^2 \cdot y^6 = y^{2 + 6}=y^8\).

Step3: Combine with the coefficient

The coefficient is \(-6\), so combining with the simplified x and y terms, we get \(-6x^4y^8\).

Answer:

\(-6x^4y^8\) (the third option: \(-6x^4y^8\))