Answer:
[tex]15x^4y^5z^2[/tex]
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)(a^c) = a^(b+c)
[tex]3xy^4z^2\cdot 5x^2yx=(3\cdot 5)x^{1+2+1}y^{4+1}z^2=15x^4y^5z^2[/tex]
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Comment on the rule of exponents
You can see where the rule comes from when you consider that an exponent signifies repeated multiplication.
x² = x·x . . . . . . the 2 signifies that x is a factor 2 times
x³ = x·x·x . . . . the 3 signifies that x is a factor 3 times
The product of these is ...
(x²)(x³) = (x·x)(x·x·x) = x·x·x·x·x = x⁵ = x²⁺³
