Question

Please help me solve this?

Answer 1

`15x^4y^5z^2`

Explanation:

The applicable rule of exponents is ...

(a^b)(a^c) = a^(b+c)

`3xy^4z^2\cdot 5x^2yx=(3\cdot 5)x^(1+2+1)y^(4+1)z^2=15x^4y^5z^2`

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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