12. $$ -2 p^{3} q^{-3} $$ for $$ p=3 $$ and $$ q=-2 $$

Question

UpStudy AI · Accepted Answer

Substitute $$ p = 3 $$ and $$ q = -2 $$ into the expression:
$$
-2 p^3 q^{-3} = -2 \times 3^3 \times (-2)^{-3}
$$

Calculate $$ 3^3 $$:
$$
3^3 = 27
$$

Calculate $$(-2)^{-3}$$ using the negative exponent rule:
$$
(-2)^{-3} = \frac{1}{(-2)^3} = \frac{1}{-8} = -\frac{1}{8}
$$

Now substitute the values back into the expression:
$$
-2 \times 27 \times \left(-\frac{1}{8}\right)
$$

Multiply:
$$
-2 \times 27 = -54
$$
$$
-54 \times \left(-\frac{1}{8}\right) = \frac{54}{8}
$$

Simplify the fraction by dividing numerator and denominator by $$2$$:
$$
\frac{54 \div 2}{8 \div 2} = \frac{27}{4}
$$

Thus, the value of the expression is:
$$
\frac{27}{4}
$$
The value of the expression is $$ \frac{27}{4} $$.

12. \( -2 p^{3} q^{-3} \) for \( p=3 \) and \( q=-2 \)