The problem asks us to determine if the two given expressions, $(5p^3q)(4p^5q^9)$ and $20p^8q^{10}$, are equivalent.

1. Problem Description

The problem asks us to determine if the two given expressions, $(5p^3q)(4p^5q^9)$ and $20p^8q^{10}$, are equivalent.

2. Solution Steps

We need to simplify the first expression, $(5p^3q)(4p^5q^9)$, and then compare it to the second expression, $20p^8q^{10}$.

To simplify the first expression, we multiply the coefficients and add the exponents of the same variables:

$(5p^3q)(4p^5q^9) = (5 \cdot 4)(p^3 \cdot p^5)(q \cdot q^9)$

When multiplying terms with the same base, we add the exponents:

$x^m \cdot x^n = x^{m+n}$

Therefore, $p^3 \cdot p^5 = p^{3+5} = p^8$ and $q \cdot q^9 = q^{1+9} = q^{10}$.

So, $(5p^3q)(4p^5q^9) = (20)(p^8)(q^{10}) = 20p^8q^{10}$.

Now we compare the simplified expression $20p^8q^{10}$ with the second expression $20p^8q^{10}$. Since they are identical, the expressions are equivalent.

3. Final Answer

Yes