Maths Questions ! Fast PLz~

1)
3^(x+1) + 3^x - 108 = 0
3*3^x + 3^x = 108
(3 + 1)*3^x = 108
4*3^x = 108
3^x = 27
3^x = 3^3
x = 3


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2)
6^-2x - [2^(2-x)] [3^(2-x)] = 0
6^-2x - 6^(2-x) = 0
6^-2x = 6^(2-x)
-2x = 2 - x
x = -2


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3)
3^(10a+7) - 27^(5a-1) = 0
3^(10a+7) - (3^3)^(5a-1) = 0
3^(10a+7) - 3^(15a-3) = 0
3^(10a+7) = 3^(15a-3)
10a + 7 = 15a - 3
5a = 10
a = 2


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4)
[(m^-1 n)^2 (m n^-2)^-2 ] / (m^-3 n^-4)
= [(m^-2 n^2) (m^-2 n^4)] / (m^-3 n^-4)
= m^[(-2)+(-2)-(-3)] n^[2+4-(-4)]
= m^-1 n^10
= n^10 / m


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5)
[(2^(n+1)) + 5(2^n)] / 49(2^-n )
= (2*2^n + 5*2^n) / 49*2^-n
= (2 + 5)*2^n / 49*2^-n
= (7/49)*2^[n-(-n)]
= 2^2n / 7


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6)
(80 000 000 * 0. 000 0005) / 0.00002
= (8 * 10^7) * (5 * 10^-7) / (2 * 10^-5)
= (8*5/2) * 10^[7+(-7)-(-5)]
= 20 * 10^5
= 2 000 000


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7)
( 0.49 * 10^-5) / ( 700 * 10^-20)
= (4.9 * 10^-6) / (7 * 10^-18)
= (4.9/7) * 10[(-6)-(-18)]
= 0.7 * 10^12
= 7 * 10^11