Evaluate the expression $a^2\cdot a^5$ if $a= 3$.
The given expression equals $a^{2+5}=a^7$. Plugging in the value of $a$, the expression equals $3^7=\boxed{2187}$.
2187
Level 1
Algebra
Problem: Evaluate the expression $a^2\cdot a^5$ if $a= 3$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To evaluate the expression $a^2 \cdot a^5$, I need to apply the properties of exponents. According to the laws of exponents, when multiplying two expressions with the same base, I can add their exponents. Here, the base is $a$, and the exponents are $2$ and $5$. 

First, I calculate the sum of the exponents: 
2 + 5 = 7. 

This means that $a^2 \cdot a^5$ can be rewritten as $a^7$. 

Next, I substitute the value of $a$ into the expression. Since $a = 3$, I need to evaluate $3^7$. 

To compute $3^7$, I can break it down into smaller steps:
3^1 = 3,
3^2 = 3 \cdot 3 = 9,
3^3 = 3 \cdot 9 = 27,
3^4 = 3 \cdot 27 = 81,
3^5 = 3 \cdot 81 = 243,
3^6 = 3 \cdot 243 = 729,
3^7 = 3 \cdot 729 = 2187.

Thus, the final answer is $2187$.<|END_OF_LATENT|> The final answer is $2187$.