We have : 7 x ab x ad = abcd

Smallest a and b is 1 and 0

We have 7 x 1 x 0 x 1 x d = 1 x 0 x c x d

Smallest c and d is 0

We have 7 x 1 x 0 x 1 x 0 = 1 x 0 x 0 x 0

Smallest abcd is 1000

\(\dfrac{x-1}{x^3+x}=\dfrac{-1}{x^3}\)

We have: 145+176+147+167+198+132+150+141+138+143+146=1683

She have $1485 so: 1683-1485=198

So we remove the Birthday (Katty Perry): 198$

\(A=\dfrac{2^{40}.3^{50}.25^4.9}{4^{21}.9^{25}.3^2.5^8}\)

\(A=\dfrac{2^{40}.3^{50}.\left(5^2\right)^4.3^2}{\left(2^2\right)^{21}.\left(3^2\right)^{25}.3^2.5^8}\)

\(A=\dfrac{2^{40}.3^{50}.5^8.3^2}{2^{42}.3^{50}.3^2.5^8}\)

\(A=\dfrac{1}{2^2}=\dfrac{1}{4}\)

Hey how much is it equal to?