It looks like you're working on simplifying expressions using the power rule of exponents! The power rule states that \((a^m)^n = a^{m \cdot n}\). Let's clarify and simplify the expressions you provided step by step.
Given expressions:
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\(6^8\)
Your answer: \((74)^8\) — This doesn't match, as \(6\) and \(74\) are not equivalent. -
\(73^{20}\)
Your answer: \(10^{63}\) — This doesn't match. -
\(78^{48}\)
Your answer: \((4^5)^2\) — This doesn't match. -
\(12^6\)
Your answer: \(15^{12}\) — This doesn't match. -
You didn't provide the expression for this; just the answer \(8\).
Now let's go through them step by step:
-
Power of 6: \(6^8\) remains \(6^8\) (there's no simplification).
-
Power of 73: \(73^{20}\) remains \(73^{20}\) (again, no simplification).
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Power of 78: \(78^{48}\) remains \(78^{48}\) (no simplification).
-
Power of 12: \(12^6\) remains \(12^6\) (no simplification).
-
The expression before this point is unclear, please provide it.
If you have specific expressions in mind or need clarification for simplification or application of the power rule, let me know!