Question

question
fully simplify.
answer attempt 1 out of 2
$x^{5}y^{2}(2x^{2})$

Explanation:

Step1: Simplify the power of 2

First, we simplify \((2x^{2})\). According to the power of a product rule \((ab)^n = a^n b^n\), we have \((2x^{2}) = 2^1\times(x^{2}) = 2x^{2}\) (wait, actually, if it's \((2x^{2})\) without an exponent, maybe the original problem is \(x^{5}y^{2}(2x^{2})\)? Wait, maybe the original expression is \(x^{5}y^{2}\times(2x^{2})\)? Let's assume that. So first, multiply the coefficients and the like - bases.

The coefficient is 2 (from \(2x^{2}\)) and we have \(x^{5}\) and \(x^{2}\), and \(y^{2}\).

Step2: Multiply the coefficients and use the exponent rule for multiplication

For the coefficients: we have 1 (from \(x^{5}y^{2}\)) and 2 (from \(2x^{2}\)), so \(1\times2 = 2\).

For the \(x\) terms: using the rule \(a^{m}\times a^{n}=a^{m + n}\), for \(x^{5}\times x^{2}\), we get \(x^{5 + 2}=x^{7}\).

For the \(y\) terms: we have \(y^{2}\) and no other \(y\) terms, so it remains \(y^{2}\).

Putting it all together, we have \(2\times x^{7}\times y^{2}=2x^{7}y^{2}\).

Answer:

\(2x^{7}y^{2}\)