Question

Simplify the expression. Write your answer as a power.

Answer 1

Answer:

(-4).(-4) = 4^2

Step-by-step explanation:

First, some rules that we need to remember:

if A is a positive number, then:

-A = (-1)*A

Also:

A*A = A^2

We also should remember that we can multiplicate in any order we want, this is:

A*B*C = (A*B)*C = A*(B*C)

And we also can change the order of the numbers:

A*B = B*A

And finally, we need to remember the sign rules for multiplication.

(+)*(+) = (+)

(+)*(-) = (-)

(-)*(+) = (-)

(-)*(-) = (+)

Ok, now let's look at our expression.

(-4)*(-4)

First, we can rewrite this as:

( (-1)*4)*((-1)*4)

And we can rearrange the numbers to:

(-1)*(-1)*4*4

Now let's multiplicate the first two ones, because of the sign rule, we know that the outcome will be positive, and 1 times 1 is equal to 1,

(-1)*(-1) = 1

Then:

(-1)*(-1)*4*4 = 1*4*4 = 4*4

And we know that when a number is multiplied by itself we can rewrite it as:

4*4 = 4^2

Then:

(-4).(-4) = 4^2

The simplified expression is 4^2