Law 5: Zero Index

Topic Content:

This law states that any number raised to the power of zero (0) equals 1.

Worked Example 5.5.1:

Simplify the following;

a. \( \scriptsize 4^{0} \)

b. \( \scriptsize\left( 5^6\right)^{0} \)

c. \( \scriptsize 5^2 \: \times \: 5^{-2}\)

d. \( \scriptsize 2^5 \: \div \: 2^{5}\)

e. \( \scriptsize 8a^0 \: \div \: 8^{0}\)

Solution

a. \( \scriptsize 4^{0} = 1\)

b. \( \scriptsize\left( 5^6\right)^{0} = 1 \)

c. \( \scriptsize 5^2 \: \times \: 5^{-2} \\ \scriptsize =5^{2-2} \\ \scriptsize = 5^0 \\ \scriptsize = 1\)

d. \( \scriptsize 2^5 \: \div \: 2^{5} \\ \scriptsize = 2^{5-5} \\ \scriptsize = 2^0 \\ \scriptsize = 1\)

e. \( \scriptsize 8a^0 \: \div \: 8^{0} \\ \scriptsize 8 \: \times \: a^0 \: \div \: 8^0 \\ \scriptsize = 8 \: \times \: 1 \: \div \: 1\\ \scriptsize = 8 \: \div \: 1 \\ \scriptsize = 8\)

Evaluation Questions: