How to Find the Base of a Number


To find a number's base, it helps to have some background knowledge of powers. Powers are composed of bases and exponents. For example, 222 produces a result of 8. Since the number 2 is multiplied by itself 3 times, we can say that 2 to the third power, or 2^3, equals 8. Hence, an exponent, in this case 3, dictates the number of times to multiply the base by itself.

Things You'll Need

  • Scientific or graphing calculator equipped with ^ button
  • Identify the parts of the problem. An equation of this type is composed of three elements -- the base, an exponent and a known quantity. The base is the unknown and is denoted with a variable such as x or y. The exponent is a small number in superscript written to the right of the base. The base and exponent are separated from the known quantity by an equals sign. For instance, in x^5=1024, the base is x, the exponent is 5 and the known number is 1024.

  • Take the exponent and reciprocate it. To reciprocate a fraction, simply reverse its numerator and denominator. For example, reciprocating the number 5 produces 1/5.

  • Divide this fraction on your calculator to obtain a decimal. Dividing 1/5 produces 0.2. Make note of this decimal. Alternatively, if your calculator is equipped with parentheses buttons, you can skip this step and leave the reciprocal as a fraction.

  • Type the known number into your calculator. Press the "^" button. Then type either the decimal from step 3 or the reciprocal from step 2 enclosed by a set of parentheses. Following the previous example, you would type 1024^0.2 or 1024^(1/5). Press the "enter" or "equals" key. The resultant number is your base. In x^5=1024, the base, x, is 4. This means that 4^5, or 44444, equals 1024.


  • Photo Credit Mathematik image by bbroianigo from
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