Multiplying indices

When we multiply two indices with the same base, we can simply add the powers. This can be written as:

a^x\times a^b=a^{x+y}

Example: simplify x^3\times x^{-2}

Example: evaluate 2^4\times 2^3

Example: evaluate 5^0\times 5^3

Example: evaluate 7^2\times 7^{-5}

Example: simplify y\times y^{-4}

flashcards

QuestionAnswer
rule for multiplying two same-base indicesWhen multiplying indices with the same base, add the powers: a^x\times a^b=a^{x+y}
simplify x^3\times x^{-2}x^3\times x^{-2} = x^{3+-2} = x^{3-2} = x^1 = x
evaluate 2^4\times 2^32^4\times 2^3 = 2^{4+3} = 2^7 = 128
evaluate 5^0\times 5^35^0\times 5^3 = 5^{0+3} = 5^3 = 125
evaluate 7^2\times 7^{-5}7^2\times 7^{-5} = 7^{2+-5} = 7^{-3} = \frac{1}{7^3} = \frac{1}{343}
simplify y\times y^{-4}y\times y^{-4} = y^{1+-4} = y^{-3} or \frac{1}{y^3}