Question

Write your answer as a power or as a product of powers. $$ 3^{4} \cdot 3^{6} $$

Short answer

The solution is \(3^{10}\).

Step-by-step solution

Identify the base

The common base for both powers is 3.

Add the exponents

According to the laws of exponents, when you multiply like bases, you add the exponents. Therefore, you add the exponent of \(3^{4}\), which is 4, and the exponent of \(3^{6}\), which is 6. The sum of 4 and 6 is 10.

Write the answer as a power

Having added the exponents correctly, you can now present the answer as a power. The base is still 3, and the new exponent is 10. Hence, the result is \(3^{10}\).