Dividing indices

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

a^x\div a^b=a^{x-y}

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

• =x^{3--2}
• =x^{3+2}
• =x^5

Example: evaluate 2^7\div 2^3

• =2^{7-3}
• =2^4
• =16

Example: evaluate 5^3\div 5^0

• =5^{3-0}
• =5^3
• =125

Example: simplify y^4\div y

• =y^{4-1}
• =y^3