Solve for

Question

\[x\].
\[5^x=5^3\cdot5^8\]
\[x=\]

Answer 1

Using the property of exponents that $a^m \cdot a^n = a^{m+n}$, we can simplify the right side to $5^{3+8} = 5^{11}$. Hence, $x=\boxed{11}$.

Answer 2

Solve for
\[x\].
\[5^x=5^3\cdot5^8\]
\[x=\]

Answer 3

Since both sides of the equation have the same base ($5$), we can set the exponents equal to each other and solve for $x$. So we have $x = 3 + 8 = \boxed{11}$.

Answer 4

Simplify.
Rewrite the expression in the form
\[4^n\].
\[4^4\cdot 4^3=\]

Answer 5

Using the property of exponents that $a^m \cdot a^n = a^{m+n}$, we can simplify the right side to $4^{4+3} = 4^7$. Therefore, \[4^4 \cdot 4^3 = \boxed{4^7}.\]