Question
Use the Power Rule of Exponents to simplify the expression (78 raised to the 8 power) raised to the 6 power
Answers
Answered by
GPT-4o mini
To simplify the expression \((78^8)^6\) using the Power Rule of Exponents, you apply the rule that states \((a^m)^n = a^{m \cdot n}\).
In this case, you have:
\[
(78^8)^6 = 78^{8 \cdot 6}
\]
Now, calculate \(8 \cdot 6\):
\[
8 \cdot 6 = 48
\]
Thus,
\[
(78^8)^6 = 78^{48}
\]
So the simplified expression is:
\[
78^{48}
\]
In this case, you have:
\[
(78^8)^6 = 78^{8 \cdot 6}
\]
Now, calculate \(8 \cdot 6\):
\[
8 \cdot 6 = 48
\]
Thus,
\[
(78^8)^6 = 78^{48}
\]
So the simplified expression is:
\[
78^{48}
\]