i could use some math help

Question

Use the quotient property of exponents to simplify this expression, write the answer with positive exponents only.

(3y_^17/(3y)^9

Answer 1

Since the exponents does not include the coefficients it is good to factor them out.

 

(3y17)/(3y9) =( 3/3⁸ ) ( y17/y9 )  =(3^-8)( y¹⁷y^-9)

        

= (3^-8 y^{17 - 9} =  y⁸ / 6561

 

Ans:    y = y8 / 6561

Answer 2

Note that the 3's are included in the parenthesis in both numerator

and denominator and thus are also raised to the exponents 17 and 9

respectively.

 

(3y)¹⁷/(3y)⁹ = (3y)¹⁷(3y)^-9 = (3y)^17-9 = (3y)⁸ = 3⁸y⁸ = 6561y⁸

Answer 3

Helllo Jay,

 

Remember when dividing or multiplying, tackle the coefficients separately from the variables.  And if there is more than one variable, i.e. an x and a y, handle them separately as well.  When multiplying, you add the exponents; when dividing you subtract the exponents.

 

(3y¹⁷)/(3y⁹) = (3/3) (y¹⁷/y⁹) = y⁸