Answer :
To simplify the expression [tex]\(-x \cdot 4x^9\)[/tex], we can follow these steps:
1. Identify the terms: We have two terms in the product: [tex]\(-x\)[/tex] and [tex]\(4x^9\)[/tex].
2. Multiply the coefficients: The coefficients are the numerical parts of the terms. Here, the coefficients are [tex]\(-1\)[/tex] from [tex]\(-x\)[/tex] and [tex]\(4\)[/tex] from [tex]\(4x^9\)[/tex]. Multiply these together:
[tex]\[
-1 \times 4 = -4
\][/tex]
3. Multiply the variables: Look at the variable part, which is [tex]\(x\)[/tex] in both terms. When you multiply variables with the same base, you add their exponents. The first term, [tex]\(-x\)[/tex], has an exponent of 1, written as [tex]\(x^1\)[/tex], and the second term is [tex]\(x^9\)[/tex]. So, you add the exponents:
[tex]\[
x^1 \cdot x^9 = x^{1+9} = x^{10}
\][/tex]
4. Combine the results: Combine the result of the coefficients and the variables:
[tex]\[
-4 \cdot x^{10}
\][/tex]
So, the product in its simplest form is [tex]\(-4x^{10}\)[/tex].
1. Identify the terms: We have two terms in the product: [tex]\(-x\)[/tex] and [tex]\(4x^9\)[/tex].
2. Multiply the coefficients: The coefficients are the numerical parts of the terms. Here, the coefficients are [tex]\(-1\)[/tex] from [tex]\(-x\)[/tex] and [tex]\(4\)[/tex] from [tex]\(4x^9\)[/tex]. Multiply these together:
[tex]\[
-1 \times 4 = -4
\][/tex]
3. Multiply the variables: Look at the variable part, which is [tex]\(x\)[/tex] in both terms. When you multiply variables with the same base, you add their exponents. The first term, [tex]\(-x\)[/tex], has an exponent of 1, written as [tex]\(x^1\)[/tex], and the second term is [tex]\(x^9\)[/tex]. So, you add the exponents:
[tex]\[
x^1 \cdot x^9 = x^{1+9} = x^{10}
\][/tex]
4. Combine the results: Combine the result of the coefficients and the variables:
[tex]\[
-4 \cdot x^{10}
\][/tex]
So, the product in its simplest form is [tex]\(-4x^{10}\)[/tex].
