Q: Are there two irrational numbers where one is raised to the power of the other and the answer is a rational number?

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1,000,000,000 = 1 x 109 The rules of writing a number in this scientific notation are : M x 10N , where M is a rational decimal number between 0 and 10 and N is the Power of Ten it is raised to.

A number raised to the second power is a number times itself. This can also be stated as a number squared.

To have exactly 9 factors, the number would either have to have a prime number raised to the 8th. power; this is not possible with two digits.The other option is to have a prime number raised to the second power, times another prime number raised to the second power. (The number of factors in this case is (2 + 1)(2 + 1).) This is only possible if you use the prime factors 2 and 3; any other combination of prime numbers will yield a number that has more than 2 digits.

The power could then be called an exponent. The number that is being raised to a power is called the base. In the case of 42, the exponent is 2 and the base is 4.

Related questions

Some irrational numbers can be multiplied by another irrational number to yield a rational number - for example the square root of 2 is irrational but if you multiply it by itself, you get 2 - which is rational. Irrational roots of numbers can yield rational numbers if they are raised to the appropriate power

No.

Rational!!!! Casually, any decimal that can be converted to a fraction/ratio is Rational. 1.1 = 1 1/10 = 11/10 Irrational numbers are those that cannot be converted to a fraction/ration. The most well known IRRATIONAL number is 'pi = 3.141592....' Irrational numbers are those were the decimals go to infinity AND the decimal digits are not in any regular order. Rational ; 1/3 = 0.3333.... Irrational ; sqrt(2) = 1.414213562....

yes

' 1 ' raised to any power = 1 .The power can be a whole number, a fraction, a decimal,positive, or negative, rational or irrational.

Yes (when the power is a positive integer). It is possible to have powers that are negative, rational, irrational and even complex and there are similar rules for dealing with them.

Yes.

Yes.

Not necessarily. The value of 3 (rational) raised to the power 1/2 (rational) is not rational.

In the number x, with positive integer exponent a, a is the number of times that 1 (not the number itself) is multiplied by x. So, for example in the expression, 43 the exponent is 3 and the number represented is "1 is multiplied by 4 three times". If you multiply 4 by itself 3 times, you will get 4*4 (one time) * 4 (two times) *4 (three times) and that is NOT 43: it is just a wrong description.The laws of exponents are:xa * xb = xa+bxa / xb = xa-b(xa)b = xa*b(xy)a = xa * yaThe first three are used to extend the domain of exponents to negative integers and rational numbers. Exponents to irrational numbers are defined as limits of the exponents of the rational sequences converging to the irrational number.Finally, 00 is not defined (because it does not converge).

The raised number, or exponent, is the number of times the base is used as a factor.

For example:The number called "e", which is approximately 2.71828... (the base of the natural logarithm, and of the exponential function).The square root of any positive integer that isn't a perfect square (the square root of 2, 3, 5, 6, 7, 8, 10, etc.).The cubic root of any positive integer that isn't a perfect cube.Any irrational number multiplied by a rational number except zero, for example 2 x pi, (1/5) times the square root of 2, etc.A rational number raised to a rational power is USUALLY irrational, for example, 10 to the power 0.5 (which is the same as the square root of 10), 10 to the power 0.17, etc.