Prove that `(frac(cosx+isinx)(sinx+icosx))^5=cos(10x-frac(5pi)(2))+isin(10x-frac(5pi)(2))`

(frac(2)(3))^(-5)= ?

7(cos((-5pi)/6)+isin((-5pi)/6))=?

(frac(-2)(5))^(7) div (frac(-2)(5))^(5)= ?

(frac(-1)(5))^(3) div (frac(-1)(5))^(8)= ?

The value of (sin frac(pi)(8) + i cos frac(pi)(8))^(8)/((sin frac(pi)(8) - i cos frac(pi)(8))^(8)) is :

(frac(-2)(3))^(10) div (frac(-2)(3))^(8)= ?

Prove that : int_(0)^(pi//2) (cos^(5))/(sin^(5) x+cos^(5) x)dx= (pi)/(4)

Write each of the following in power notation: ( i ) frac(5)(7)xxfrac(5)(7)xxfrac(5)(7)xxfrac(5)(7) ( ii ) (frac(-4)(3)) xx (frac(-4)(3)) xx (frac(-4)(3)) xx (frac(-4)(3)) xx (frac(-4)(3)) ( iii ) (frac(-1)(6)) xx (frac(-1)(6)) xx (frac(-1)(6)) ( iv ) (-8) xx (-8) xx (-8) xx (-8) xx (-8)

Find x such that: (i) frac(-1)(5)=frac(8)(x) (ii) frac(7)(-3)=frac(x)(6) (iii) frac(3)(5)=frac(x)(-25) (iv) frac(13)(6)=frac(-65)(x) (v) frac(16)(x)=-4 (vi) frac(-48)(x)=2

Simplify and express each of the following as a rational number: ( i ) (frac(3)(2))^(-3) xx (frac(3)(2))^(-2) ( ii ) (frac(3)(4))^(-2) xx (frac(5)(2))^(-3) ( iii ) (frac(-2)(3))^(-4) xx (frac(-3)(5))^(2)