Express answer with positive exponents only

Question

16x⁵x³y⁵ 

_______

 

28x¹³y^-2

Answer 1

16x⁵x³y⁵

-----------

28x¹³y^-2

 

First look at the constants (coefficients).. plain numbers

 

16/28 can be reduced by a factor of 4

16/28 = 4/7

 

Look at the x varaibles:

 

x⁵x³/x¹³ = x⁸/x¹³

Both can be reduced by a factor of. x⁸

x⁸/x¹³ = x8/x⁸x⁵ = 1/x⁵

 

Look at the y variables:

y⁵/y^-2 

Note:  x^-n= 1/xⁿ

and 1/x^-n = xⁿ

Thus;  1/y^-2 = y²

 

So: y⁵/y^-2 = y⁵y² = y⁷

 

putting this back together:

 

16x⁵x³y⁵           4y⁷

-----------   = --------

28x¹³y^-2.           7x⁵

 

Answer 2

This equation is a fraction, which is another form of

division (numerator divided by the denominator).

When there are exponents, look at the variables,

and for identical variables, subtract the exponents

(numerator exponents - denominator exponents).

If the result is negative, place the variable, with

exponent solution in the denominator, but as a

positive exponent.

If the result is positive, place it in the numerator.

Now, putting it into motion (you can handle the 16/28)

x variables: x⁵ * x³ = x⁵⁺³ = x⁸

  x⁸ - x¹³ = x^-5

  place as x⁵ in the denominator

y variables: y^{5 - (-2)} = y⁵⁺² = y⁷

  leave in the numerator as y⁷

 

Go Get Your "A"