10x^3y^-2 over 15x^6y^-3 this equation is then the ^-3

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samhouston | Middle School Teacher | (Level 1) Associate Educator

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First, separate the constant and the two variables and simplify.

10 / 15 = 2 / 3

x^3 / x^6 = 1 / x^3

y^-2 / y ^-3 (negative exponents - switch the numerator and denominator)

y^3 / y^2 = y^1 / 1

Now combine these three terms.

Numerator:  2 * 1 * y^1 = 2y

Denominator:  3 * x^3 * 1 = 3x^3

The entire fraction is to the power of -3.  Because the exponent is negative, switch the numerator and denominator.

Numerator:  3x^3

Denominator:  2y

Now distribute the exponent of 3 to all terms.

Numerator:  (3x^3)^3 = 27x^9

Denominator:  (2y)^3 = 8y^3

Final answer:  27x^9 / 8y^3 

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