Law of indices

• What is the definition of an index or power in mathematics?


  It shows how many times a number has been multiplied by itself.
• How is the expression $2^4$ expanded?


  $2^4 =$$2 \times 2 \times 2 \times 2$
• What is the law of indices for multiplication?


  • When multiplying like bases:
  • $a^m \times a^n =$$a^{(m+n)}$
  • Example:
  • $c^3 \times c^2 =$$c^5$
• What is the result of $b^5 \div b^2$?


  $b^3$
• How is $b^5 \div b^3$ simplified?


  $b^5 \div b^3 =$$b^{5-3} =$$b^2$
• What is the law of indices for division?


  • When dividing like bases:
  • $a^m \div a^n =$$a^{(m-n)}$
• What is the result of $(k^2)^3$?


  $k^6$
• How is $(k^y)^z$ simplified?


  $(k^y)^z =$$k^{yz}$
• What is the rule for powers to powers in indices?


  • When raising a power to another power:
  • $(a^m)^n =$$a^{(mn)}$
• What is the value of $J^0$?


  1
• What does $J^5 \div J^5$ equal?


  1
• What is the summary of the laws of indices?


  • Multiplication: $a^m \times a^n =$$a^{(m+n)}$
  • Division: $a^m \div a^n =$$a^{(m-n)}$
  • Power to Power: $(a^m)^n =$$a^{(mn)}$
  • Power of Zero: $a^0 =$$1$
• How is a negative index expressed in terms of a fraction?


  $d^{-n} =$$\frac{1}{d^n}$
• What is the result of $d^4 \div d^5$?


  $d^{-1}$
• What happens when there are negative indices?


  • Negative indices become fractions:
  • $d^{-n} =$$\frac{1}{d^n}$
• What is the general rule for decimals in indices?


  Decimals can be expressed as sums or products in indices.