Powers of powers (maths)

• What is the process for raising a term like \( p^2 \) to another power, such as 3?


  Multiply the term \( p^2 \) by itself three times.
• What does the exponent in a power indicate?


  It indicates how many times to multiply the base by itself.
• How can \( p^2 \) raised to the power of 3 be expressed in terms of \( p \)?


  It can be expressed as \( p^6 \).
• How do you derive \( p^6 \) from \( (p^2)^3 \)?


  By multiplying the exponents: \( 2 \times 3 = 6 \).
• What is \( x^3 \) raised to the power of 4?


  It is \( x^{12} \).
• What happens when one of the powers is negative, such as in \( x^2 \) raised to the power of -5?


  The technique remains the same: multiply the exponents.
• What is the result of \( x^2 \) raised to the power of -5?


  It is \( x^{-10} \).
• How can you evaluate \( 2^3 \) raised to the power of 2?


  You can either multiply the exponents or calculate \( 2^3 \) first.
• What is \( 2^3 \) raised to the power of 2 calculated directly?


  It is \( 2^6 \), which equals 64.
• How can you simplify \( 4a^3 \) raised to the power of 2?


  It simplifies to \( 16a^6 \).
• What is the process for simplifying \( 3p^{-2} \) raised to the power of 3?


  Apply the power to both the number and the variable separately.
• What is the result of \( 3p^{-2} \) raised to the power of 3?


  It is \( 27p^{-6} \).
• What are the steps to raise a power to another power?

  1. Identify the base and the exponents.
  2. Multiply the exponents together.
  3. Simplify the expression if necessary.
• How do you handle expressions with both numbers and variables raised to powers?


  • Treat numbers and variables separately.
  • Apply the exponent to both parts.
  • Simplify the results.