What is the product?

[tex]\((3a^2b^7)(5a^3b^8)\)[/tex]

A. [tex]\(8a^5b^{15}\)[/tex]
B. [tex]\(8a^6b^{56}\)[/tex]
C. [tex]\(15a^5b^{15}\)[/tex]
D. [tex]\(15a^5b^{56}\)[/tex]



Answer :

To find the product of two algebraic expressions, we need to multiply the coefficients and add the exponents of the corresponding variables.

Given the expressions:
[tex]\[ (3a^2b^7) \text{ and } (5a^3b^8) \][/tex]

### Step-by-Step Solution:

1. Multiply the coefficients:

The coefficients of the expressions are [tex]\(3\)[/tex] and [tex]\(5\)[/tex]. Multiplying these coefficients gives:
[tex]\[ 3 \times 5 = 15 \][/tex]

2. Add the exponents of [tex]\(a\)[/tex]:

The exponents of [tex]\(a\)[/tex] in the expressions are [tex]\(2\)[/tex] and [tex]\(3\)[/tex]. Adding these exponents gives:
[tex]\[ 2 + 3 = 5 \][/tex]

3. Add the exponents of [tex]\(b\)[/tex]:

The exponents of [tex]\(b\)[/tex] in the expressions are [tex]\(7\)[/tex] and [tex]\(8\)[/tex]. Adding these exponents gives:
[tex]\[ 7 + 8 = 15 \][/tex]

Combining these results, the product of the given expressions is:
[tex]\[ 15a^5b^{15} \][/tex]

Therefore, the correct product is:
[tex]\[ \boxed{15a^5b^{15}} \][/tex]