what is 12^1/4 divided by 12 ^3/4?
and what is (27/27^1/3)^1/2?
thanks! showing your steps would be awesome.
and what is (27/27^1/3)^1/2?
thanks! showing your steps would be awesome.
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OK ????
#1. You have the same base so 12^(1/4)/12^(3/4) is = 12^(1/4-3/4) = 12^(-1/2) = 1/12^(1/2) but teachers don't like to see radicals in the denominator so multiply both top and bottom by 12^(1/2)
and you get 12^(1/2)/12 and this simplifies to sqrt(3)/6.
#2. (27/27^1/3)^1/2?? check the denominator of what's in the ( ). 27^1/3 = 3 so (27/3)^1/2 = 9^1/2 = 3. Remember PEMDAS and look for simplifications within the ( ) before going further.
#1. You have the same base so 12^(1/4)/12^(3/4) is = 12^(1/4-3/4) = 12^(-1/2) = 1/12^(1/2) but teachers don't like to see radicals in the denominator so multiply both top and bottom by 12^(1/2)
and you get 12^(1/2)/12 and this simplifies to sqrt(3)/6.
#2. (27/27^1/3)^1/2?? check the denominator of what's in the ( ). 27^1/3 = 3 so (27/3)^1/2 = 9^1/2 = 3. Remember PEMDAS and look for simplifications within the ( ) before going further.
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It is so because you are not making the use of required number of parentheses. Remember the following rule about them. " more the merrier!
12^1/4 divided by 12 ^3/4 = 12^{(1/4) - (3/4)} = 12^(-2/4)or
= 12^(-1/2 = 1/{(12)^(1/2)} = 1/√(12)= 1/√(4*3) = 1/{2*√(3)} =√(3)/{2*√(3)√(3)} = √(3)/6
12^1/4 divided by 12 ^3/4 = 12^{(1/4) - (3/4)} = 12^(-2/4)or
= 12^(-1/2 = 1/{(12)^(1/2)} = 1/√(12)= 1/√(4*3) = 1/{2*√(3)} =√(3)/{2*√(3)√(3)} = √(3)/6
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[27/{27^(1/3)}]^(1/2) = [27/{(3^3)}^(1/3)}]^(1/2) = [27/3]^(1/2) = 9^(1/2) = 3
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The "rules of exponents" are a hugh part of Algebra and are usually contained in their own chapter of any math book. They are easy to learn and usually spelled out very well in the textbook.
Read them and learn them.
Learn how to subtract the exponents when dividing like bases (problem one)
Learn how to multiply the exponents when raising a power to a power like in problem number two
Learn how to move a number vertically within a fraction to change a negative exponent to a positive exponent.
Read them and learn them.
Learn how to subtract the exponents when dividing like bases (problem one)
Learn how to multiply the exponents when raising a power to a power like in problem number two
Learn how to move a number vertically within a fraction to change a negative exponent to a positive exponent.
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when you divide exponents with the same base you just subtract the esponents. So the first question is 12^(-2/4) = 12^(-1/2)=1/(12^(1/2))