4th root as an exponent FIrst off we cannot have a negative on any of our even roots square 4th 6th etc without getting into imaginary numbers So if you are asking 5 1 5 we could write the square root sign with a raised 5 on the crook of the root sign and a 5 inside
The solutions of x 4 16 are called fourth roots of 16 and are written x pm sqrt 4 16 It is extremely important to note the symmetry in Figure 3 c and note that we have two real solutions of x 4 16 one of which is negative and the other positive Hence we need two notations one for the positive fourth root of 16 and Learn how to convert a radical to rational power A radical is an expression having the root radical symbol The number outside the radical symbol nth r
4th root as an exponent
4th root as an exponent
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As a counter example for the third rule a m n a m n if a 0 and n is a fraction we could have 3 2 1 2 means do 3 2 9 first then find square root 9 1 2 3 However 3 2xx 1 2 means do 2xx 1 2 1 When raising a power to a power you multiply the exponents but the bases have to be the same Because raising a power to a power means that you multiply exponents as long as the bases are the same you can simplify the following expressions Leave the exponent as 9 4 Don t write it as a mixed number
The order does not matter so it also works for m n 1 n m x m n x 1 n m x 1 n m n x m And we get this A fractional exponent like m n means Do the m th power then take the n th root xm n n xm or Take the n th root then do the m th power xm n n x m Some examples What is 4 th root The 4th root of a number is the number that would have to be multiplied by itself 4 times to get the original number What is exponent 4 The exponent 4 of a number is found by multiplying that number by itself 4 times Similar Tables 4th Root 5th Root 6th Root 7th Root 8th Root 9th Root 10th Root 11th Root 12th Root
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The base is the factor and the positive integer exponent indicates the number of times the base is repeated as a factor In the above example the base is 5 and the exponent is 4 In general if a is the base that is repeated as a factor n times then Figure PageIndex 1 When the exponent is 2 we call the result a Fourth Root sqrt 4 text number indicates the fourth root of the number under the radical sign sqrt 4 81 3 since 3 cdot 3 cdot 3 cdot 3 3 4 81
I suggest you read Fractional Exponents first so this makes more sense Anyway the important idea is that x 1 n The n th Root of x And so a fractional exponent like 4 3 2 is really saying to do a cube 3 and a square root 1 2 in any order Just remember from fractions that m n m 1 n Algebra Write in Exponential Form fourth root of x 3 4 x3 x 3 4 Use n ax ax n a x n a x n to rewrite 4 x3 x 3 4 as x3 4 x 3 4 x3 4 x 3 4 Free math problem solver answers your algebra geometry trigonometry calculus and statistics homework questions with step by step explanations just like a math tutor
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4th root as an exponent - The order does not matter so it also works for m n 1 n m x m n x 1 n m x 1 n m n x m And we get this A fractional exponent like m n means Do the m th power then take the n th root xm n n xm or Take the n th root then do the m th power xm n n x m Some examples