Q&A for How to Solve Decimal Exponents

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  • Question
    Why do you calculate the root before the exponent?
    David Jia
    Academic Tutor
    David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
    Academic Tutor
    Expert Answer
    You can do either one first, but it's easier to take the root first because it will give you a smaller number, which will be easier to work with in your head.
  • Question
    How can you easily calculate a decimal exponent?
    David Jia
    Academic Tutor
    David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
    Academic Tutor
    Expert Answer
    First, take the decimal and convert it to a fraction. The numerator of the fraction is an exponent and the denominator is going to be a root. For example, if you have a number like 8^2/3, you would take the cube root of 8 first, which is 2, then square that to get 4.
  • Question
    How do I find 15^1.4?
    Top Answerer
    First convert 1.4 to 14/10, and reduce to 7/5. An exponent of 7/5 means first raising to the seventh power and then finding the fifth root (or first finding the fifth root and then raising to the seventh power). Thus, in this case you would raise 15 to the seventh power and then find that number's fifth root.
  • Question
    How do I solve .4 to the 4th power?
    Top Answerer
    (.4)^4 = (.4)(.4)(.4)(.4) = .0256. Another way to do it is to express .4 as 4 x 10^-1. Thus (4 x 10^-1)^4 = 4^4 x 10^-4 = 256^-4 = .0256.
  • Question
    How to calculate 2^1/7 without using a calculator?
    Top Answerer
    That's the seventh root of 2, and unless your mind is exceptionally good at doing calculations, it's not realistic to expect to solve that without a rather powerful calculator.
  • Question
    .3^1/3 - how do I solve this type of question?
    Top Answerer
    .3^1/3 means the cube root of (.3). 3^2/3 means the cube root of 3². Thus, with a fractional exponent, the numerator of the exponent indicates an actual exponent, and the denominator of the exponent indicates a root.
  • Question
    Larson, Algebra and Trigonometry, 8th edition, page 24, gives a warning that (-8)^(2/6) does not exist, even though (-8)^(1/3). You say simplify first. He says don't. What should I do?
    Top Answerer
    This is a unique situation. While the cube root of -8 does exist, the sixth root of -8 does not exist, because it's an imaginary number (√-2). So in this case the exponent 2/6 is not equivalent to the exponent 1/3. In a classroom setting an instructor can decide whether or not to define two such exponents as equivalent and then simplify.
  • Question
    How would I do 0.174?
    Top Answerer
    0.174 = 174/1000 = 87/500. An exponent of 87/500 indicates the 500th root of the 87th power of whatever the base number is.
  • Question
    How do I solve .833^2.63?
    Top Answerer
    It would take a very powerful computer to solve that. First the exponent would have to be converted to the improper fraction 263/100. Then .833 would have to be expanded to the 263rd power, and then you'd have to find the 100th root of that number.
  • Question
    If the exponent is in decimal and negative form, how can I solve?
    Community Answer
    If the decimal is negative, like in 5^-2, simply ignore the negative sign and solve. Then divide the answer into 1. So, the above problem would equal 1/25. 4^-3 would equal 1/64. Fraction exponents are more complex. The numerator would be solved first, and the denominator is a root. So, 4^2/3 would be the cube root of 16.
  • Question
    How do I solve 2^1.4? The answer is 2.638, but I don't know how to get it.
    Top Answerer
    An exponent of 1.4 is an exponent of 14/10, reduced to 7/5. That means raising a number to its seventh power, and then finding that number's fifth root. The seventh power of 2 is 128. The fifth root of 128 is 2.639.
  • Question
    In the first equation, how did they get 1/4? I am not understanding this, it just seems like they threw it in there and didn't explain!
    Top Answerer
    What they're doing is breaking the exponent 3/4 into two parts, ¼ and 3, which when multiplied together make 3/4. So they're saying the base (81) will first be raised to the power of ¼ and then be raised again to the power of 3. In this case that means first finding the fourth root of 81, which is 3, and then raising that 3 to the power of 3, which is 27.
  • Question
    How do I expand a number using exponents?
    Top Answerer
    Multiply the number by itself one time fewer than the number in the exponent. For example, 8^6 means multiplying 8 times 8 five times. Put another way, 8 would be a factor six times in the answer: 8 x 8 x 8 x 8 x 8 x 8 = 262,144.
  • Question
    How do I do quadruple roots?
    Top Answerer
    The fourth root is the square root of the square root.
  • Question
    2^1\24 how I will simplify it?
    Top Answerer
    2^(1/24) equals the 24th root of 2. You can't "simplify" it beyond that.
  • Question
    What is [1.047]^10?
    Community Answer
    Raising x to the tenth power means using x as a factor ten times (which means multiplying x by itself nine -- not ten -- times). (1.047)^10 = 1.583.
  • Question
    What is 3^1/2?
    Community Answer
    3^(1/2) is the same thing as the square root of 3. √3 = 1.73.
  • Question
    How do I find 2.51 to the power of .1?
    Community Answer
    You're looking for the tenth root of 2.51. You would need a root calculator for this. You can find one online by searching "nth root calculator".
  • Question
    (5/3) base and exponent is 1/6. How do you solve this?
    Community Answer
    You're looking for the sixth root of (5/3), which is the sixth root of 5 divided by the sixth root of 3. It takes a calculator to do this. Try savvycalculator.com/sixth-root-calculator.
  • Question
    What is 10^1.2?
    Community Answer
    10^(1.2) = 10^(1 2/10) = 10^(1 1/5) = 10^(6/5), which is the fifth root of 10^6.
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