Question

question
fully simplify.
8xy(x^{3}y)

Explanation:

Step1: Use distributive property (multiply coefficients and variables)

First, multiply the coefficient \( 8 \) with the terms inside the parentheses. Then, for the variables with the same base, use the exponent rule \( a^m \cdot a^n = a^{m + n} \).

For the \( x \)-terms: \( x \cdot x^3 = x^{1 + 3} = x^4 \) (since when multiplying variables with the same base, we add the exponents; \( x = x^1 \), so \( 1 + 3 = 4 \))

For the \( y \)-terms: \( y \cdot y = y^{1 + 1} = y^2 \) (similarly, \( y = y^1 \), so \( 1 + 1 = 2 \))

The coefficient remains \( 8 \).

Step2: Combine the results

Multiply the coefficient with the simplified variable terms: \( 8 \times x^4 \times y^2 = 8x^4y^2 \)

Answer:

\( 8x^4y^2 \)