Question

question
fully simplify.
$10x^3(x^2y^3)$

Explanation:

Step1: Use the distributive property (multiply coefficients and like variables)

We know that when multiplying monomials, we multiply the coefficients and add the exponents of like - base variables. For the coefficient, we have 10 (since there is no other coefficient inside the parentheses, we can consider the coefficient inside the parentheses as 1). For the \(x\) terms, we have \(x^{3}\) and \(x^{2}\). According to the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), when we multiply \(x^{3}\) and \(x^{2}\), we get \(x^{3+2}\). For the \(y\) term, we just carry it over as it is (since there is no other \(y\) term to multiply with in terms of adding exponents, we can think of it as \(y^{3}\times y^{0}\), and \(y^{0} = 1\), so \(y^{3+0}=y^{3}\)).
So, \(10x^{3}(x^{2}y^{3})=10\times(x^{3}\times x^{2})\times y^{3}\)

Step2: Simplify the exponents of \(x\)

Using the exponent rule \(a^{m}\times a^{n}=a^{m + n}\), for \(x^{3}\times x^{2}\), we have \(m = 3\) and \(n=2\), so \(x^{3}\times x^{2}=x^{3 + 2}=x^{5}\)

Step3: Combine the results

Now we combine the coefficient and the simplified variable terms. The coefficient is 10, the \(x\) term is \(x^{5}\) and the \(y\) term is \(y^{3}\). So we get \(10\times x^{5}\times y^{3}=10x^{5}y^{3}\)

Answer:

\(10x^{5}y^{3}\)