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How do you multiply # (2x^4)/ (10y^2) * ( 5y^3)/(4x^3)#?

Answer 1

Eli Assouline

#(2x^4)/(10y^2)*(5y^3)/(4x^3)#

I simplify "in cross" the two cohefficients:

#(2x^4)/(2y^2)*(y^3)/(4x^3) # (simplified 10 and 5)

#(x^4)/(y^2)*(y^3)/(2x^3)# (simplified 4 and 2)

Now I multiply the variables together and I order them to work properly:

#(x^4y^3)/(2x^3y^2)#

Assuming that #x!=0# and #y!=0#, I can reduce the degree of the variables in this way:

#(x^(4-3)*y^(3-2))/(2*x^(3-3)*y^(2-2))#

That is basically:

#(xy)/2#

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Answer 2

Jace Anderson

To multiply the given expressions, you can multiply the numerators together and the denominators together.

(2x^4 * 5y^3) / (10y^2 * 4x^3)

Simplifying the numerator and denominator separately:

Numerator: 2 * 5 = 10, x^4 * y^3 = x^(4+3) = x^7, so the numerator becomes 10x^7.

Denominator: 10 * 4 = 40, y^2 * x^3 = y^(2+3) = y^5, so the denominator becomes 40y^5.

Therefore, the final answer is:

(10x^7) / (40y^5)

This can be simplified further by dividing both the numerator and denominator by their greatest common factor, which is 10:

x^7 / (4y^5)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.