To simplify the expression [tex]\((7x^5)(8x)\)[/tex], let's follow a step-by-step approach:
1. Identify coefficients and variable parts
- The first term is [tex]\(7x^5\)[/tex]. Here, [tex]\(7\)[/tex] is the coefficient and [tex]\(x^5\)[/tex] is the variable part.
- The second term is [tex]\(8x\)[/tex]. Here, [tex]\(8\)[/tex] is the coefficient and [tex]\(x\)[/tex] is the variable part.
2. Multiply the coefficients
- Multiply the coefficients of the two terms: [tex]\(7\)[/tex] and [tex]\(8\)[/tex]:
[tex]\[
7 \times 8 = 56
\][/tex]
3. Multiply the variable parts
- Multiply the variable parts which are in exponential form: [tex]\(x^5\)[/tex] and [tex]\(x\)[/tex].
- When multiplying variables with exponents, you add the exponents:
[tex]\[
x^5 \times x = x^{5+1} = x^6
\][/tex]
4. Combine the results
- Combine the product of the coefficients with the product of the variable parts:
[tex]\[
56 \times x^6 = 56x^6
\][/tex]
So, the simplified expression is [tex]\(56x^6\)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{56x^6} \][/tex]
- Option A. [tex]\(56x^5\)[/tex] is incorrect because the exponent of [tex]\(x\)[/tex] should be [tex]\(6\)[/tex], not [tex]\(5\)[/tex].
- Option B. [tex]\(15x^6\)[/tex] is incorrect because the coefficient should be [tex]\(56\)[/tex], not [tex]\(15\)[/tex].
- Option C. [tex]\(56x^6\)[/tex] is correct.
