use the power rule of exponents to simplify the expression (78^8) ^6

Answer 1

To simplify the expression \((78^8)^6\) using the power rule of exponents, we apply the rule which states that \((a^m)^n = a^{m \cdot n}\).

In this case, we have:

\[ (78^8)^6 = 78^{8 \cdot 6} \]

Now calculate \(8 \cdot 6\):

\[ 8 \cdot 6 = 48 \]

Therefore, the simplified expression is:

\[ (78^8)^6 = 78^{48} \]

So the final answer is:

\[ 78^{48} \]