Exponents Practice Questions and Tutorial

Exponents may seem like advanced math —like some mysterious code with a complicated meaning. In fact, though, an exponent is just short hand for saying that you’re multiplying a number by itself two or more times. For instance, instead of saying that you’re multiplying 5 x 5 x 5, you can show that you’re multiplying 5 by itself 3 times if you just write 5³ .We usually say this as “five to the third power” or “five to the power of three.” In this example, the raised 3 is an “exponent,” while the 5 is the “base.”

You can even use exponents with fractions. For instance, ½ ³ means you’re multiplying ½ x ½ x ½. (The answer is 1/8). Some other helpful hints for working with exponents:

• Here’s how to do basic multiplication of exponents. If you have the same number with a different exponent (For instance 5³ X 5²  ) just add the exponents and multiply the bases as usual. The answer, then, is 25⁵ .
• This doesn’t work, though, if the bases are different. For instance, in 5³  X 3²   we simply have to do the math the long way to figure out the final solution: 5 x 5 x 5,  multiplying that result times the result for 3 X 3. (The answer is 1125).

• Looking at it from the opposite side, to divide two exponents with the same base (or bottom number), subtract the smaller exponent from the larger one. If we were dividing the problem above, we would subtract the 2 from the 3 to get 1.  5 to the power of 1 is simply 5.
• One time when thinking of exponents as merely multiplication doesn’t work is when the raised number is zero. Any number raised to the “zeroth” power is 1 (Not, as we tend to think, zero).