Respuesta :
p(x) * r(x) = ab^x * cd^x
p(x) * r(x) = (a*c)*(b^x*d^x)
p(x)*r(x) = ac(bd)^x
For the last step, I used the rule that (ab)^x = a^x*b^x
Final Answer: ac(bd)^x
The value of p(x).r(x) = [tex]ac(bd)^x[/tex]. This is obtained by multiplying the given functions and applying the law of exponents.
What are the laws of exponents?
Some of the basic laws of exponents are:
- [tex]a^m .a^n =a^(^m^+^n^)[/tex] (multiplying two exponents with the same base results in the addition of their powers)
- [tex]a^-^1=\frac{1}{a^n}[/tex] (inverse of 'a' results in the reciprocal of 'a')
- [tex]a^m.b^m=(ab)^m[/tex] (multiplying two exponents with the same power results in the power of the product of their bases)
Calculating the given product:
Given that,
p(x) = [tex]ab^x[/tex] and r(x) = [tex]cd^x[/tex]
Then,
p(x) × r(x) = ([tex]ab^x[/tex]) × ([tex]cd^x[/tex])
= [tex]ac(b^xd^x)[/tex]
Since the powers are the same, we can use the law of exponent [tex]a^m.b^m=(ab)^m[/tex], we get
p(x) × r(x) = [tex]ac(bd)^x[/tex]
Therefore, the value of the given product is [tex]ac(bd)^x[/tex].
Learn more about laws of exponents here:
https://brainly.com/question/11975096
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