How to Calculate Decimal Exponents

Once you have mastered integer exponents, the next topic to master is rational exponents. Decimal exponents are merely an extension of that topic. Mastering decimal exponents is necessary for many advanced mathematical applications. Mechanical and aeronautical engineering equations repeatedly require calculations involving decimal exponents. Most engineering calculators can solve problems with decimal exponents, but as with any other mathematical process, it is important to learn how to do the calculations manually to fully understand the results.

Things You'll Need

• Basic understanding of rational exponents

Instructions

1. Convert the decimal exponent to a rational exponent. If the decimal exponent is 1.2, the rational equivalent will be 12/10. Reducing the fraction by factorization simplifies it to 6/5, since the prime factor "2" can be divided out of both the numerator and denominator.

2. Solve the numerator portion of the problem. In this case, the problem started as x^(1.2), which can be rewritten as x^6/5. The numerator of the exponent is "6," so the solution to this part of the problem is x^6. This is now the base for the rest of the problem.

3. Complete the problem by solving the denominator portion of the problem. In this example, the denominator is "5." This means you need to take the fifth root of the base, which was found to be x^6. The complete solution is "fifth root of x^6."

Resources

• West Texas A&M University lesson on rational exponents