Problem 23 - Elementary Algebra

Question

\(\left(u^{2}\right)^{7}\)

Step-by-Step Solution

Answer

u^{14}

Step 1: Understand the Power Rule

Recall the exponentiation rule \( (a^m)^n = a^{mn} \). This rule states that when raising a power to another power, you multiply the exponents.

Step 2: Apply the Power Rule

Identify the inner and outer exponents in the expression \( (u^2)^7 \). The inner exponent is 2 and the outer exponent is 7.

Step 3: Perform the Multiplication

Multiply the inner exponent by the outer exponent: \( 2 \times 7 = 14 \).

Step 4: Write the Final Expression

Using the result from the multiplication, the expression \( (u^2)^7 \) simplifies to \( u^{14} \).

Key Concepts

Exponentiation

Exponentiation is a mathematical operation that involves raising a number, called the base, to a certain power. This is done using an exponent or index. For example, in the expression \(u^2\), \