The product of the algebraic expressions [tex]3a^{2}b^7[/tex] and [tex]5a^3b^8[/tex] is [tex]15a^5b^{15}[/tex]. Hence, 3rd option is the right choice.
How do we multiply two algebraic expressions?
When two algebraic expressions are multiplied, the like terms are to be combined and multiplied, and then they should be written as a single algebraic expression.
How do we solve the given question?
In the question, we are asked to find the product of the algebraic expressions [tex]3a^{2}b^7[/tex] and [tex]5a^3b^8[/tex], that is:
([tex]3a^{2}b^7[/tex])([tex]5a^3b^8[/tex]).
To find the product of the two expressions, we combine the like terms:
[tex](3*5)(a^2*a^3)(b^7*b^8)[/tex]
= [tex](15)(a^5)(b^{15})[/tex] (Using the law of exponents: [tex]x^a*x^b = x^{a+b}[/tex])
Now we write them as a single expression: [tex]15a^5b^{15}[/tex].
∴ The product of the algebraic expressions [tex]3a^{2}b^7[/tex] and [tex]5a^3b^8[/tex] is [tex]15a^5b^{15}[/tex]. Hence, 3rd option is the right choice.
Learn more about the product of algebraic expressions at
https://brainly.com/question/4344214
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