Question

Rewrite the exponential expression below using a single base.
Start with the first expression. How can you rewrite the exponential expression below using a single base?
5
3
·6
3
=

Answer 1

To rewrite the expression \( 5^3 \cdot 6^3 \) using a single base, we can observe that both terms are raised to the power of 3. This allows us to factor out the exponent:

\[
5^3 \cdot 6^3 = (5 \cdot 6)^3
\]

Now, we can simplify the base:

\[
5 \cdot 6 = 30
\]

So, the expression can be rewritten as:

\[
5^3 \cdot 6^3 = 30^3
\]

Thus, \( 5^3 \cdot 6^3 = 30^3 \).