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simplify ....

(6^x/2 × 12^x+1 × 27^− x/2)/32^x/2
Reply 1
Its more clear here
Please use brackets to make the expression clearer. The first term can be interpreted as 6^(x/2) or (6^x)/2 and it's very confusing.

If I interpreted it correctly as 6^(x/2), then multiplying each term with a common term of x, you can simply add the powers. So e.g. axmbxn=abxmxn=abxm+nax^m * bx^n = a * b * x^m * x^n = ab * x^{m+n}
After looking at the picture, just do what I said for the numerator. Then use similar law of indices to divide the numerator by the denomator:
axmbxn=abxmxn=ab(xnm)ora(xmn)b\frac{ax^m}{bx^n} = \frac{a}{b} * \frac{x^m}{x^n} = \frac{a}{b(x^{n-m})} or \frac{a(x^{m-n})}{b}
(edited 5 years ago)
Reply 4
Original post by E--
Its more clear here

Notice how the negative exponent on the 27 is equal to the exponent of the 32, you can just manipulate and it use your law of indices to simplify, for example
42x62x=162x42x=1242x\frac{4^{-2x}}{6^{2x}}=\frac{1}{6^{2x}4^{2x}}=\frac{1}{24^{2x}}
For the numbers which have the exact same exponent in the the numerator and denominator, you can use your laws to simplify, for example
163x323x=(1632)3x=(12)3x\frac{16^{3x}}{32^{3x}} = \left(\frac{16}{32}\right)^{\:3x} = \left(\frac{1}{2}\right)^{\:3x}

That is all you will need, well the way i solved the question is by using those two tricks :wink:, post your working here if you are stuck
(edited 5 years ago)
Reply 5
Original post by Azim Patel
Notice how the negative exponent on the 27 is equal to the exponent of the 32, you can just manipulate and it use your law of indices to simplify, for example
42x62x=162x42x=1242x\frac{4^{-2x}}{6^{2x}}=\frac{1}{6^{2x}4^{2x}}=\frac{1}{24^{2x}}
For the numbers which have the exact same exponent in the the numerator and denominator, you can use your laws to simplify, for example
163x323x=(1632)3x=(12)3x\frac{16^{3x}}{32^{3x}} = \left(\frac{16}{32}\right)^{\:3x} = \left(\frac{1}{2}\right)^{\:3x}

That is all you will need, well the way i solved the question is by using those two tricks :wink:, post your working here if you are stuck

i'm getting 112x+1\frac{1}{12^{x+1}} ?
but the answer should just be 12
(edited 5 years ago)
Original post by E--
i'm getting 112x+1\frac{1}{12^{x+1}} ?
but the answer should just be 12

Show your working out please
try collecting all the terms with a power of x/2.

then simplify and see what you've got
Reply 8
Write U = (x/2). Split the 6 into 2x3 and split the 12.
You should wind up with 2x2x3 = 12

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