# Math

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Compute the following

-7/2 x 9^-3/2 + 3/2 x 9^-5/2 + 14

7/2 is a negative fraction.
the entire fractions are multiplied by 9 raised to their respective exponents. I can't figure this out. Please help?

• Math -

Since 9 = 3^2, 9^1/2 = 3

-7/2 * 9^-3/2 = (-7/2) / (9^3/2) = -7/(2*3^3)

3/2 * 9^-5/2 = (3/2) / (9^5/2) = (3/2) / 3^5 = 1/(2*3^4)

So, now we have

-7/(2*3^3) + 1/(2*3^4) + 14
= (-7*3 + 1 + 14*2*3^4)/(2*3^4)
= 2248/162
= 1124/81

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