Question

SIMPLIFYING EXPRESSIONS Simplify. Write your answer as a power or as an expression containing powers. $$\left(3^{6}\right)^{3}$$

Short answer

The simplified form of \((3^{6})^{3}\) is \(3^{18}\)

Step-by-step solution

Identify the base and the exponents

The expression \((3^{6})^{3}\) has a base of 3. The first exponent is 6 and then this result is raised to the power of 3.

Apply the rule of exponents

According to the rule of exponents, \((a^{m})^{n} = a^{mn}\), the exponents should be multiplied when a power is raised to another power. Here, you need to multiply 6 and 3 to get the final exponent.

Simplify the expression

Multiply the exponents. \(6 \times 3 = 18\). So, \((3^{6})^{3} = 3^{18}\)