Verified answer

(4/9)^-1/2

= 1/(4/9)^1/2

= (9/4)^1/2

= rt9 / rt4

= 3/2.

This one is tricky. Watch carefully:

The negative exponent means the whole number must go into the denominator. But we have a fraction. How do we do this? The exponent does become positive, but the negative exponent tells us to take the reciprocal of the fraction. We end up with:

(9/4) ^1/2

Now, take the square root of the fraction:

= 3/2

Miss Kristin

a) (5^4 / 9) ^ -a million/2 = a million / {(5^4 / 9) ^ a million/2} = a million / sqrt { (5^4 / 9) } = a million / { 5 ^2 / 3} = 3 / (5 ^ 2) = 3 / 25 b) i think of ur question is ( a million + x ) / x = ?3 a million + x = ?3 * x Squaring on the two aspects, we get, (a million + x)^2 = (?3 * x)^2 a million^2 + x^2 + 2(a million)(x) = (?3)^2 * x^2 a million + x^2 + 2x = 3x^2 3x^2 = x^2 + 2x + a million 3x^2 - x^2 - 2x - a million = 0 2x^2 - 2x - a million = 0 Use the formulation under: For ax^2 + bx + c = 0, the answer is x = { -b + sqrt [ b^2 - 4ac ] } /2a x = { -b - sqrt [ b^2 - 4ac ] } /2a right here, a = 2, b = -2 and c = -a million. So, b^2 - 4ac = (-2)^2 - 4(2)(-a million) = 4+8 = 12 sqrt(12) = sqrt(4*3) = 2*sqrt(3) hence, x = {-(-2) + 2*sqrt(3)} / [2(2)] and x = {-(-2) - 2*sqrt(3)} / [2(2)] x = {2 + 2*sqrt(3)} / 4 and x = {2 - 2*sqrt(3)} / 4 x = 2{a million + sqrt(3)} / 4 and x = 2{a million - sqrt(3)} / 4 x = {a million + sqrt(3)} / 2 and x = {a million - sqrt(3)} / 2 answer: x = (a million+?3)/2 and x = (a million-?3)/2

Firstly, a number to the power of a negative is the reciprocal, so e.g. (4/9)^-1 becomes 1/(4/9)^1. Secondly, a number to the power of a fraction is the root of the denominator, e.g. (4/9)^1/2 becomes square root of 4/9. As a result, (4/9)^-1/2 should become 1/square root (4/9) although i would check, but I'm confident it's that.