Evaluate each expression. $$ \begin{array}{ll} ext { 5. }(-6)^{-5} & ext { 6. } 8^{-4}\end{array} $$

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Evaluate each expression. $$ \begin{array}{ll}	ext { 5. }(-6)^{-5} & 	ext { 6. } 8^{-4}\end{array} $$

UpStudy AI · Accepted Answer

1. For $$ (-6)^{-5} $$:
   - Rewrite the expression using the negative exponent rule:
     $$
     (-6)^{-5} = \frac{1}{(-6)^5}
     $$
   - Evaluate $$ (-6)^5 $$. Since 5 is odd, the result will be negative:
     $$
     (-6)^5 = -(6^5) = -7776
     $$
   - Thus:
     $$
     (-6)^{-5} = \frac{1}{-7776} = -\frac{1}{7776}
     $$

2. For $$ 8^{-4} $$:
   - Rewrite the expression using the negative exponent rule:
     $$
     8^{-4} = \frac{1}{8^4}
     $$
   - Evaluate $$ 8^4 $$:
     $$
     8^4 = 4096
     $$
   - Thus:
     $$
     8^{-4} = \frac{1}{4096}
     $$
$$ (-6)^{-5} = -\frac{1}{7776} $$ and $$ 8^{-4} = \frac{1}{4096} $$.

Evaluate each expression. \( \begin{array}{ll}\text { 5. }(-6)^{-5} & \text { 6. } 8^{-4}\end{array} \)

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