Question

\\(7y^5 x^7 \cdot 2y^{-2} x^3\\)

Explanation:

Identify the expression to simplify

The given expression in the image is:

$$ 7x^5 y^7 \cdot 2y \cdot 2x^3 $$

Group coefficients and variables

Rearrange the terms to group the numerical coefficients, the \(x\) variables, and the \(y\) variables together:

$$ (7 \cdot 2 \cdot 2) \cdot (x^5 \cdot x^3) \cdot (y^7 \cdot y^1) $$

Simplify each group using exponent rules

Calculate the product of the coefficients and apply the product rule for exponents \(a^m \cdot a^n = a^{m+n}\):

$$
LATEXBLOCK0
$$

Combine the simplified parts:

$$ 28x^8 y^8 $$

Answer:

The simplified form of the expression \(7x^5 y^7 \cdot 2y \cdot 2x^3\) is <blank>\(28x^8 y^8\)</blank>.