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If x^2 y^3 = 10 and x^3 y^2 = 8, what is the value of x^5 y^5

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Explanation:

so,

x²y³ = 10

x³y² = 8

what is the value of x⁵y⁵ ?

don't you see right away that 2+3 and 3+2 both equal 5 ?

so, x³x² = x⁵

y²y³ = y⁵

so, I only need to multiply both equations with each other. and I get

x²y³×x³y² = 10×8

x⁵y⁵ = 80

why ? because multiplications and exponents (which are nothing else than multiplications) are all communicative :

a×b = b×a.

User Matthewelsom
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