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}

• =x^{3+-2}
• =x^{3-2}
• =x^1
• =x

Example: evaluate 2^4\times 2^3

• =2^{4+3}
• =2^7
• =128

Example: evaluate 5^0\times 5^3

• =5^{0+3}
• =5^3
• =125

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

• =7^{2+-5}
• =7^{-3}
• =\frac{1}{7^3}
• =\frac{1}{343}

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

• =y^{1+-4}
• =y^{-3} or \frac{1}{y^3}