Answer:
[tex]\frac{1}{r^{42}}[/tex] is equivalent to [tex](r^{-7})^6[/tex]
Step-by-step explanation:
Using the exponent rule:
[tex](a^n)^m = a^{nm}[/tex]
[tex]a^{-n} = \frac{1}{a^n}[/tex]
Given the radical expression:
[tex](r^{-7})^6[/tex]
Apply the rule we have;
[tex]r^{-7 \cdot 6}[/tex]
Simplify:
[tex]r^{-42}[/tex]
Again, apply the rule:
[tex]\frac{1}{r^{42}}[/tex]
Therefore, the expression is equivalent to [tex](r^{-7})^6[/tex]
[tex]\frac{1}{r^{42}}[/tex].
