Question

Which is the value of this expression when p = negative 2 and q = negative 1?

((p squared) (q Superscript negative 3 Baseline)) Superscript negative 2 Baseline times ((p Superscript negative 3 Baseline) (q superscript 5 Baseline)) Superscript negative 2
–4
Negative StartFraction 1 Over 16 EndFraction
StartFraction 1 Over 16 EndFraction
4

Answer 1

Let's evaluate the expression step-by-step with \( p = -2 \) and \( q = -1 \).

The expression we have is:

\[
\left( (p^2)(q^{-3}) \right)^{-2} \times \left( (p^{-3})(q^5) \right)^{-2}
\]

### Step 1: Evaluate \( p^2 \) and \( q^{-3} \)
First, calculate \( p^2 \):

\[
p^2 = (-2)^2 = 4
\]

Now calculate \( q^{-3} \):

\[
q^{-3} = (-1)^{-3} = -1
\]

Now substitute these back into the expression:

\[
\left( (4)(-1) \right)^{-2} \times \left( (p^{-3})(q^5) \right)^{-2}
\]

### Step 2: Combine the terms in the first part
Calculating the product:

\[
(4)(-1) = -4
\]

Now take this to the power of -2:

\[
\left(-4\right)^{-2} = \frac{1}{(-4)^2} = \frac{1}{16}
\]

### Step 3: Evaluate \( p^{-3} \) and \( q^5 \)
Next, calculate \( p^{-3} \) and \( q^5 \):

\[
p^{-3} = (-2)^{-3} = -\frac{1}{8}
\]
\[
q^5 = (-1)^5 = -1
\]

Now substitute these values into the second part:

\[
\left( (-\frac{1}{8})(-1) \right)^{-2}
\]

### Step 4: Combine the terms in the second part
Calculating the product:

\[
(-\frac{1}{8})(-1) = \frac{1}{8}
\]

Now take this to the power of -2:

\[
\left(\frac{1}{8}\right)^{-2} = 8^2 = 64
\]

### Step 5: Final Expression
Now we multiply the two parts together:

\[
\frac{1}{16} \times 64
\]

Calculate the final value:

\[
\frac{64}{16} = 4
\]

Thus, the value of the expression when \( p = -2 \) and \( q = -1 \) is

\[
\boxed{4}
\]