We want to evaluate the given expressions,
and then check with the graphing calculator.
For our first example,
we have x to the power of negative two.
We want to evaluate this for x equals four.
So performing this substitution,
we would have four raised to the power of negative two.
And now from here, to simplify this,
let's rewrite this with the positive exponent.
To do this, let's create a fraction with
the denominator of one.
Now if we move four to the negative two,
to the denominator, it changes the sign of the exponent.
So this is equal to one divided by four,
raised to the power of positive two.
Well four squared is equaled to 16,
so that's simplifies to one 16th.
Checking on the calculator, we have four raised
to the power of negative two, enter.
To convert this to a fraction, we press,
math enter enter, verifying our answer.
Next we have two v raised to the power of negative three.
We want to evaluate this for v equals negative three.
Performing this substitution we'd have, two times the base
of negative three, raised to the power of negative three.
Notice how here we have two to the first
times negative three raised to the power of negative three.
Let's rewrite this with positive exponents.
We'll create a fraction with the denominator of one.
If we move negative three raised to the power
of negative three to the denominator,
it'll change the sign of the exponent.
The two stays in the numerator.
We'd have two divided by the base of negative three
raised to the power of positive three.
Negative three to the third is negative three times
negative three times negative three,
which is equal to negative 27.
We have two divided by negative 27, and notice our fraction
is negative, so it's more common to write
this as negative two 27th's.
Let's check this.
We have two, open parenthesis negative three
closed parenthesis, raised to the power of negative three
enter, and then math enter enter.
Again, verifying our answer.
Our first two answers look good.
Next, we have three c raised to the power of negative two,
and notice here that the base is three c.
Pefrorming this substitution, we'd have in parenthesis three
times three raised to the power of negative two.
Three times three is nine, so we'd have nine raised
to the power of negative two.
Writing this with a positive exponent,
we can create a fraction with the denominator of one.
We'll move nine to the power of negative two down to the
denominator, which will change the sign of the exponent.
This is equal to one over nine raised to
the power of positive two or nine squared.
Nine times nine is equal to 81, so we have one over 81
for the value of our expression.
Checking on the calculator, open parenthesis three times
three, and all this is raised to the power of negative two.
Enter, and math enter enter, again verifying our answer.
For our last expression, we have three times 2z raised
to the power of negative two for z equals negative two.
So, we'd have three times two times negative two,
raised to the power of negative two.
Notice inside the parenthesis, we have two times
negative two, which is negative four.
So we have three times negative four raised to
the power of negative two.
Let's rewrite this with positive exponents.
We'll first create a fraction with the denominator of one.
If we move negative four raised to the power of
negative two down to the denominator,
it changes the sign of the exponent.
This is equal to the three stays in the numerator.
So we have three divided by our denominator is negative four
raised to the power of positive two
or negative four squared.
Negative four times negative four is equal to 16,
so this simplifies to 3 16th's.
Let's go ahead and check this.
We have three and then in parenthesis,
we have two times negative two.
And this is raised to the power of negative two.
Enter and math enter enter.
Again verifying our answer is correct.
I hope you've found this helpful.