What is the exponent rule for (x^m)^n?

What is the exponent rule for (x^m)^n?

• A. x^m + n
• B. x^{mn}
• C. x^{m/n}
• D. m * n

Answer: (B)

The exponent rule for \((x^m)^n\) states that when raising a power to another power, you multiply the exponents. This is derived from the definition of exponents themselves. Specifically, when you raise \(x\) to the power of \(m\) and then raise that result to the power of \(n\), you are effectively multiplying the exponent \(m\) by \(n\). Thus, the correct expression simplifies to \(x\) raised to the power of \(m \cdot n\), which is written as \(x^{mn}\). This rule helps streamline calculations involving exponents and is fundamental in simplifying expressions in algebra and higher mathematics. Understanding this principle also aids in managing more complex problems where multiple layers of exponents are involved, making it essential for students to master these rules as they progress in math.

The exponent rule for ((x^m)^n) states that when raising a power to another power, you multiply the exponents. This is derived from the definition of exponents themselves. Specifically, when you raise (x) to the power of (m) and then raise that result to the power of (n), you are effectively multiplying the exponent (m) by (n). Thus, the correct expression simplifies to (x) raised to the power of (m \cdot n), which is written as (x^{mn}).

This rule helps streamline calculations involving exponents and is fundamental in simplifying expressions in algebra and higher mathematics. Understanding this principle also aids in managing more complex problems where multiple layers of exponents are involved, making it essential for students to master these rules as they progress in math.