Indicies

• What are indices also known as?

  Exponents or powers
• What does the expression $a^n$ represent?


  It represents 'a' multiplied by itself 'n' times
• In the expression $2^3$, what is the base?


  2
• In the expression $2^3$, what is the index?


  3
• What does $2^3$ mean in terms of multiplication?


  It means multiply 2 by itself 3 times: $2 \times 2 \times 2$
• What is the result of $2^3$?


  8
• What is the multiplication rule of indices?

  When multiplying powers with the same base, add the exponents
• How would you simplify $x^3 \times x^2$ using the multiplication rule?


  $x^{3+2} =$$x^5$
• What is the division rule of indices?

  When dividing powers with the same base, subtract the exponents
• How would you simplify $\frac{x^5}{x^2}$ using the division rule?


  $x^{5-2} =$$x^3$
• What does the power of a power rule state?

  When raising a power to another power, multiply the exponents
• What is the value of $9^{\frac{1}{2}}$?


  3.
• What is the value of $16^{\frac{1}{2}}$?


  4.
• How do you calculate $27^{\frac{1}{3}}$?


  It equals 3 because 3 × 3 × 3 = 27.
• What does $8^{\frac{1}{3}}$ represent?


  The cube root of 8.
• What is the general rule for fractional indices?


  $x^{\frac{1}{n}} =$$\sqrt[n]{x}$
• What do fractional indices represent?

  They represent roots using exponent notation.
• Simplify $3^{-2}$ using the rule for negative indices.


  $\frac{1}{9}$