Simplify express your answer as a single term using exponents $178 for the power of 5 78 with the power of 9 equal
To simplify the expression $178^5 \cdot 78^9,$ we can first rewrite it as $(178\cdot78)^5 \cdot 78^4.$ Since $178\cdot78=13884,$ we have $(178\cdot78)^5 \cdot 78^4=13884^5 \cdot 78^4.$
To simplify further, we can use the property $(a\cdot b)^n=a^n\cdot b^n$ to express $13884^5 \cdot 78^4$ as $(13884^5 \cdot 78^4)=(13884^5)\cdot(78^4).$
Calculating $13884^5$ and $78^4$ separately, we find that $13884^5=408303798870334576,$ and $78^4=45653376.$
Thus, $(13884^5)\cdot(78^4)=408303798870334576\cdot45653376.$
Combining the products, we get the simplified answer: $\boxed{18657611967561594838157312}.$