Question

simplify the expression.

\\((4q^2r^2)(4q^5r^3)\\)

\\(?q^{\box}r^{\box}\\)

Explanation:

Identify the components of the expression

We are given the expression:

$$ (4q^2r^2)(4q^5r^3) $$

To simplify this, we group the coefficients, the \(q\) terms, and the \(r\) terms together.

Group coefficients and like variables

Using the Simplifying Monomials knowledge point

$$ (4 \cdot 4) \cdot (q^2 \cdot q^5) \cdot (r^2 \cdot r^3) $$

Multiply the coefficients

Using the Simplifying Monomials knowledge point

$$ 4 \cdot 4 = 16 $$

Apply the product rule for exponents

To multiply powers with the same base, we add their exponents:

$$ q^2 \cdot q^5 = q^{2+5} = q^7 $$

$$ r^2 \cdot r^3 = r^{2+3} = r^5 $$

Combine the simplified parts

Using the Simplifying Monomials knowledge point

$$ 16q^7r^5 $$

Answer:

Simplify the expression.

$$ (4q^2r^2)(4q^5r^3) $$

<blank>16</blank>\(q\)<blank>7</blank>\(r\)<blank>5</blank>