Multiply the base, the number that precedes the exponent symbol, the caret (^), by itself a number of times equal to the exponent. Conclude that for the number 10, that 10^3 is equivalent to the number 1 followed by three zeros, or 1,000. Also conclude that 10^5 is the number 1 followed by five zeros or 100,000. Remember that the number of zeros rule only works for the number 10 when it is followed by an exponent. Don't use this rule for numbers other than 10.
Calculate 2^5 as two multiplied by itself 5 times or 2*2*2*2*2, which is equal to 32.
Multiply two numbers that have positive exponents and the same base by adding the exponents and keeping the base. Calculate that (2^2)*(2^3) is equal to 2^5 since the sum of the exponents is 2 + 3, or 5.
Divide two numbers that have positive exponents and the same base by subtracting the exponents and keeping the base. Calculate that 2^5/2^2 is equal to 2^3 since subtracting the exponent in the numerator, 5, from the exponent in the denominator, 2, results in 3, and the base is 2. Calculate now that 2^5/2^2 is 8 since 2^3 is equal to 2*2*2, which equals 8.
Don't add exponents when multiplying numbers that have different bases. Instead, perform the multiplication operations on the different bases first and then multiply the results together. For example, (2^3)*(3^2) is equal to 2*2*2*3*3, which is equal to 8*9, or 72.
Don't subtract exponents when dividing numbers with exponents that have different bases. Instead, perform the exponent operation on the different bases first, then divide the result. For example, 4^3/2^3 is equal to 4*4*4/2*2*2. This is equal to 64/8, which is equal to 8.