Question

WILL GIIVE BRAINLEST AND 50PTS


Describe how you would simplify the given expression.

(20x^5y^2/5x^-3y^7)^-3

Answer 1

first, every exponent multiple by (-3), 
for x's exponent: 5*(-3)=-15, (-3)*(-3)=9, 
for y's exponent: 2*(-3)=-6, 7*(-3)=-21

Next, the exponent of the numerator (the top part) minus the exponent of the denominator:
for x:-15-9=-24
for y: -6-(-21)=15
so you have x to the -24th power, and y to the 15th power

Step 3: shift up or down the negative exponent to make it positive, now you have y to the 15th power on the top, x to the 24th power in the denominator.
 
You can simplify the constant: 20/5=4, 4 to the negative 3rd power. move it to the bottom, it becomes 4 to the positive 3rd power, which is 64
so the final result is y to the 15th power on the top, 64*x to the 24th power on the bottom.


You can also simplified what's inside the parenthesis first, then do the -3rd power part.

Answer 2

( 20x^5y² / 5x^-3y^7 ) ^-3

First, we can separate y^7.
( ( 20x^5y² / 5  x^-3) (y^7) ) ^-3

Then, expand the brackets.
x^9 / 64x^15y^27

Finally, combine like terms.
1 / 64x^6y^27