How do you multiply fractions with multiple variables and exponents?

Question

This is my problem:

(x^10)....................9(x^2)(y^2)

3(y^4) multiplied by (x^4)(y^3)

(There is no line between them, but they are both fractions.)

Answer 1

(x^10) / (3y^4) X (9(x^2)(y^2)) / (x^4)(y^3)

You multiply the two tops of the fractions together and you multiply the two bottoms (denominator) of the fractions together:

= 9[x^10*x^2*y^2] / 3[y^4*x^4y^3] Factored the 9 and the 3, so we simplify to:

= 3[x^10*x^2*y^2] / [y^4*x^4y^3]

Now lets fix the variables with different powers. Remember the rule of powers: x^a * x^b = x^(a+b)

=3[x^12 * y^2] / [y^7 * x^4]

Now its time to divide out the variables that are present on both sides of the fraction, remember the rule here: x^a / x^b = x^(a-b)

= 3[x^8] / [y^5]

Tada we're done!

Answer 2

(x^10)....................9(x^2)(y^2) -------- not understood

is it x^(10)/9(x^2)(y^2) ?

= x^(10 – 2)/9y^2

= x^8/9y^2

3(y^4) multiplied by (x^4)(y^3)

= 3y^(4+3) × x^4

= 3x^4 y^7

(x^10) / (3y^4) X (9(x^2)(y^2)) / (x^4)(y^3) arrange numerators and denominators.

= (x^10)(9(x^2)(y^2)) / (3y^4)  (x^4)(y^3)

= x^(10+2)(9y^2)/3y(4+3) x^(4)

= 9x^(12)(y^2)/3y(7) x^(4)

= 3x^(12–4)(y^2–7)

= 3x^(8)(y^–5)

= 3x^(8)/(y^5)

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