If x ≠ 0, then (x^(-7)/x^(-11))^(-1/2)

Question

If x ≠ 0, then  (\frac{x^{(-7)}}{x^{(-11)}})^{(-\frac{1}{2})}=

(A) 1/x

(B) 1/x^2

(C) x^2

(D) x^4

(E) x^9

Hero8888 · Answer

Let's work with powers only: ( -7 - (-11) )*( - 1/2 ) = -4/2 = -2. Hence 1/x^2. Answer (B).

kishorecm · Answer

(x^-7 / x^-11 ) ^ -1/2

(x^(11-7) ) ^ -1/2

(x^4)^-1/2

(1/ x^4 ) ^1/2

square root of x^4 is x^2 
= 1/x^2

generis · Answer

Rule:  a^{-n}=\frac{1}{a{^n}}

A base with a negative exponent is on the "wrong side of the fraction line." Move the base with the negative exponent to the opposite side of the fraction and remove the negative sign from the exponent.

(\frac{x^{(-7)}}{x^{(-11)}})^{(-\frac{1}{2})}=

(\frac{x^{11}}{x^{7}})^{(-\frac{1}{2})}=

(x^{(11-7)})^{(-\frac{1}{2})}=

(x^4)^{(-\frac{1}{2})}=

x^{(4*-\frac{1}{2})}=x^{-2}=\frac{1}{x^2}

Answer B

You could work this problem entirely in the denominator.

(\frac{x^{(-7)}}{x^{(-11)}})^{(-\frac{1}{2})}=

\frac{1}{x^{((-11-(-7))*\frac{1}{2})}}

(\frac{1}{x^{(4*\frac{1}{2})}})=\frac{1}{x^{2}}

Answer B

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If x ≠ 0, then (x^(-7)/x^(-11))^(-1/2)

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If x ≠ 0, then (x^(-7)/x^(-11))^(-1/2)

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