Laws of Indices Quiz

Laws of Indices

1. Product of Powers

• When multiplying two powers with the same base, add the exponents:
  • Formula: ( a^m \times a^n = a^{m+n} )
  • Example: ( 2^3 \times 2^4 = 2^{3+4} = 2^7 )

2. Power of a Power

• When raising a power to another power, multiply the exponents:
  • Formula: ( (a^m)^n = a^{m \cdot n} )
  • Example: ( (3^2)^4 = 3^{2 \cdot 4} = 3^8 )

3. Power of a Product

• When raising a product to a power, apply the exponent to each factor in the product:
  • Formula: ( (ab)^n = a^n \times b^n )
  • Example: ( (2 \times 3)^3 = 2^3 \times 3^3 = 8 \times 27 = 216 )

4. Zero Exponent Rule

• Any non-zero base raised to the power of zero is equal to one:
  • Formula: ( a^0 = 1 ) (for ( a \neq 0 ))
  • Example: ( 5^0 = 1 )

Laws of Indices

• Product of Powers: When multiplying powers with the same base, the exponents are added together. For example, multiplying ( 2^3 ) by ( 2^4 ) combines the exponents resulting in ( 2^{3+4} = 2^7 ).

• Power of a Power: To raise a power to another power, multiply the exponents. For instance, ( (3^2)^4 ) simplifies to ( 3^{2 \cdot 4} = 3^8 ).

• Power of a Product: When raising a product to a power, the exponent is distributed to each factor. For example, ( (2 \times 3)^3 ) becomes ( 2^3 \times 3^3 ), ultimately calculating to ( 8 \times 27 = 216 ).

• Zero Exponent Rule: Any non-zero base raised to the exponent of zero equals one. For example, ( 5^0 = 1 ) confirms this rule, emphasizing that only non-zero bases apply.