Calculate: $(243)^{\frac35}$
We start by finding the prime factorization of 243.  We find $243 = 3^5$, so we have $(243)^{\frac35} = (3^5)^{\frac35} = 3^{5\cdot \frac{3}{5}} = 3^3 = \boxed{27}$.
27
Level 1
Algebra
Problem: Calculate: $(243)^{\frac35}$
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve $(243)^{\frac{3}{5}}$, first recognize that 243 can be expressed as a power of 3. Specifically, $243 = 3^5$. 

Next, substitute this expression into the original problem: $(3^5)^{\frac{3}{5}}$. 

Apply the power of a power property of exponents, which states that $(a^m)^n = a^{m \cdot n}$. Here, we have $5 \cdot \frac{3}{5} = 3$. 

Thus, $(3^5)^{\frac{3}{5}} = 3^3$. 

Now, calculate $3^3$. This is equal to $3 \times 3 \times 3 = 27$. 

Therefore, the final answer is $27$.<|END_OF_LATENT|> The final answer is $27$.