The variable $a$ is jointly proportional to the cube of $b$ and the square of $c$. If $a=70$ when $b=5$ and $c=2$, what is the value of $a$ when $b=6$ and $c=6$ ? Round your answer to two decimal places if necessary. Answer 2 Points Keyboard Shortcuts

Step 1 ：The problem states that $a$ is jointly proportional to the cube of $b$ and the square of $c$. This means that $a = k \cdot b^3 \cdot c^2$, where $k$ is the constant of proportionality.

Step 2 ：We can find the value of $k$ using the given values of $a$, $b$, and $c$. Substituting $a=70$, $b=5$, and $c=2$ into the equation, we get $70 = k \cdot 5^3 \cdot 2^2$. Solving for $k$, we find that $k = 0.14$.

Step 3 ：Now we can substitute the new values of $b$ and $c$ into the equation to find the new value of $a$. Substituting $b=6$, $c=6$, and $k=0.14$ into the equation, we get $a = 0.14 \cdot 6^3 \cdot 6^2 = 1088.64$.

Step 4 ：Final Answer: The value of $a$ when $b=6$ and $c=6$ is \(\boxed{1088.64}\).