Law of indices

    Cards (16)

    • 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 242^4 expanded?

      24=2^4 =2×2×2×2 2 \times 2 \times 2 \times 2
    • What is the law of indices for multiplication?

      • When multiplying like bases:
      • am×an=a^m \times a^n =a(m+n) a^{(m+n)}
      • Example:
      • c3×c2=c^3 \times c^2 =c5 c^5
    • What is the result of b5÷b2b^5 \div b^2?

      b3b^3
    • How is b5÷b3b^5 \div b^3 simplified?

      b5÷b3=b^5 \div b^3 =b53= b^{5-3} =b2 b^2
    • What is the law of indices for division?

      • When dividing like bases:
      • am÷an=a^m \div a^n =a(mn) a^{(m-n)}
    • What is the result of (k2)3(k^2)^3?

      k6k^6
    • How is (ky)z(k^y)^z simplified?

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

      • When raising a power to another power:
      • (am)n=(a^m)^n =a(mn) a^{(mn)}
    • What is the value of J0J^0?

      1
    • What does J5÷J5J^5 \div J^5 equal?

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

      • Multiplication: am×an=a^m \times a^n =a(m+n) a^{(m+n)}
      • Division: am÷an=a^m \div a^n =a(mn) a^{(m-n)}
      • Power to Power: (am)n=(a^m)^n =a(mn) a^{(mn)}
      • Power of Zero: a0=a^0 =1 1
    • How is a negative index expressed in terms of a fraction?

      dn=d^{-n} =1dn \frac{1}{d^n}
    • What is the result of d4÷d5d^4 \div d^5?

      d1d^{-1}
    • What happens when there are negative indices?

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

      Decimals can be expressed as sums or products in indices.
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