i know the answer is 8, but i am confused how to get to that answer.
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Just pretend the equation is 4 = x^2. How do you solve this? Well, you take the square root of both sides. Alternatively, this could be thought of as raising both sides to the 1/2. You'll see that 1/2 is the reciprocal of 2. Therefore, to get rid of an exponent, just raise both sides to its reciprocal.
4 = x ^ 2/3. The reciprocal of 2/3 is 3/2, so raise both sides to the 3/2 power.
4^3/2 = x^(2/3)^(3/2). If you remember rules for raising powers to powers, you remember that you have to multiply the exponents together. Therefore, we can simplify to:
4^(3/2) = x^(6/6). Now we can see why we raised to the reciprocal: x^(6/6) cancels beautifully into just x.
4^ (3/2) = x. 4 ^(3/2) is just a fancy way of saying take the square root of 4 and raise it to the 3rd power. The square root of 4 is 2, and 2 raised to the third power = 2 * 2 * 2 = 4 * 2 = 8. Therefore, we get 4 ^ (3/2) = 8.
Just substitute and you get 8 = x.
4 = x ^ 2/3. The reciprocal of 2/3 is 3/2, so raise both sides to the 3/2 power.
4^3/2 = x^(2/3)^(3/2). If you remember rules for raising powers to powers, you remember that you have to multiply the exponents together. Therefore, we can simplify to:
4^(3/2) = x^(6/6). Now we can see why we raised to the reciprocal: x^(6/6) cancels beautifully into just x.
4^ (3/2) = x. 4 ^(3/2) is just a fancy way of saying take the square root of 4 and raise it to the 3rd power. The square root of 4 is 2, and 2 raised to the third power = 2 * 2 * 2 = 4 * 2 = 8. Therefore, we get 4 ^ (3/2) = 8.
Just substitute and you get 8 = x.
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4 = x^2/3 so to get rid of that fraction of an exponent you can raise both the 4 and the x by the reciprocal of 2/3 which is 3/2.
4^3/2 = x^(2/3)(3/2)
4^3/2 is the same as the square root of 4 raised to the 3rd power which is 2^3 or 8. x^(2/3)(3/2) is just x since when you multiply fractions by their reciprocal you always get 1.
So 8 = x. Hope that makes sense it's alot of reading but I figured the more explanation the better.
4^3/2 = x^(2/3)(3/2)
4^3/2 is the same as the square root of 4 raised to the 3rd power which is 2^3 or 8. x^(2/3)(3/2) is just x since when you multiply fractions by their reciprocal you always get 1.
So 8 = x. Hope that makes sense it's alot of reading but I figured the more explanation the better.
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Raise each side to the (3/2) power so that the right side will just be x.
Don't forget the properties
--> To raise a number already to a power to another power, keep base, multiply exponents.
--> To simplify rational(fractional) exponents, the denominator is the root, numerator is the power.
4 = x^(2/3)
4^(3/2) = x^(2/3)^(3/2)
(√4)³ = 8 = x
Don't forget the properties
--> To raise a number already to a power to another power, keep base, multiply exponents.
--> To simplify rational(fractional) exponents, the denominator is the root, numerator is the power.
4 = x^(2/3)
4^(3/2) = x^(2/3)^(3/2)
(√4)³ = 8 = x
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4 = x^(2/3)
2 = x^(1/3)
8 = x
2 = x^(1/3)
8 = x