Question

simplify the expression: (4xy)^-2

Answer 1

(4xy)^-2

Multiply x and 4

Multiply x and 1

The x just gets copied along.

The answer is x

x

4*x evaluates to 4x

Multiply y and 4x

Multiply the y and x

Multiply y and x

The y just gets copied along.

The x just gets copied along.

The answer is yx

yx

4*x*y evaluates to 4yx

The 16 becomes a 1/16
The exponent, -2, is negative, so we'll have to handle it a little bit differently here.
But for now, we'll treat it as it was positive, and handle it in the usual manner... that is, as if it were at +2.

Multiply the exponent of y by 2 giving y^2

Multiply the exponent of x by 2 giving x^2

Now, because of the negative exponent, we take this result, and turn it upside-down.
That is, a number becomes 1/the number, or a fraction is literally flipped upside-down.
This effectively "flips" the entire result upside down, but that's exactly what negative exponents do!
In this case...

The 1 becomes a 1/1
y^2 becomes 1/y^2.
x^2 becomes 1/x^2.
The answer is y^-2 x^-2

(4*x*y)^-2 evaluates to 1/16 y^-2 x^-2

Answer 2

thankyou :)

Answer 3

your welcome (: