Question

Solve for

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

[AI-generated answer — Bot GPT 3.5]

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

[AI-generated answer — Bot GPT 3.5]

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, \[4^4 \cdot 4^3 = \boxed{4^7}.\]

Answer 6

[AI-generated answer — Explain Bot]

To solve for \(x\), we can use the property of exponents which states that if two exponential expressions have the same base, then their exponents must be equal in order for the expressions to be equal.

In this case, we have the equation \(5^x = 5^3 \cdot 5^8\).

Using the property mentioned above, we can rewrite the equation as:

\(5^x = 5^{3+8}\)

Now, since the bases are the same, we can equate the exponents:

\(x = 3 + 8\)

\(x = 11\)

Therefore, \(x\) is equal to 11.