Answer:
[tex]( - 2 {x}^{4} {y}^{ - 3} )^{4} = \frac{16 {x}^{16}}{ {y}^{12} } [/tex]
Step-by-step explanation:
We want to simplify:
[tex]( - 2 {x}^{4} {y}^{ - 3} )^{4} [/tex]
We need to apply the exponential property for products of powers.
Recall that:
[tex]( {a}^{m} \times {a}^{n} )^{p} = {a}^{mp} \times {a}^{np} [/tex]
We apply this rule to get:
[tex]( - 2 {x}^{4} {y}^{ - 3} )^{4} = ( { - 2)}^{4} x \times {x}^{16} \times {y}^{ - 12} [/tex]
This simplifies to:
[tex]( - 2 {x}^{4} {y}^{ - 3} )^{4} = 16 {x}^{16} \times {y}^{ - 12} [/tex]
We rewrite as positive index to get:
[tex]( - 2 {x}^{4} {y}^{ - 3} )^{4} = \frac{16 {x}^{16}}{ {y}^{12} } [/tex]
