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the answer for the first #1 is 3/2 for the #2 its 25/16 for number #3 its 1/x^6

Step-by-step explanation

#1 apply the exponet rule a -¹ = 1/a

(2/3) ^-1 =1/2/3 Apply the fraction rule then you get 3/2

#2 (4/5)^-2 = 1/(4/5)^2 ,

(4/5)^2= 16/25

then you get your answer 25/16

#3 ((x/x^2)^3)^2 =(x/x^2) 3times 2

multiply the numbers 3 times 2 = 6

= (x/x^2)^6

(x/x^2)^6= x^6/(x^2)^6

simplify (x^2)^6: x^12

x^6/x^12(fraction)

x^6/x^12= 1/x^12-6

subtract the numbers 12-6=6

=1/x^6

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.