Problem 31 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(x^{3}\right)^{7}$$

Step-by-Step Solution

Answer

The simplified form of the given expression \( (x^{3})^{7} \) is \( x^{21} \)

Step 1: Identify the Base and Exponents

Identify the given base and exponents. Here, the base is \( x \) and the exponents are \( 3 \) and \( 7 \). The expression \( (x^{3})^{7} \) means that \( x \) is raised to the power of \( 3 \), and then the result is raised to the power of \( 7 \).

Step 2: Apply the Power of Power Rule

According to the power of a power rule, when you raise a power to another power, you should multiply the exponents together. So we multiply \( 3 \times 7 \) to get \( 21 \).

Step 3: Write the Simplified Expression

The simplified form of \( (x^{3})^{7} \) is \( x^{21} \). That is, \( x \) is raised to the power of \( 21 \).