Complete the following table :

exponent form
(-2)⁶
5¹⁰
(-3)⁴
7⁵
(-11)⁸

base ?
exponent ?

In parallelogram ABCD, AB = CD, BC = AD

Draw perpendiculars from C and D on AB as shown.

In right angled ΔAEC, AC2 = AE2 + CE2 [By Pythagoras theorem]

⇒ AC2 = (AB + BE)2 + CE2

⇒ AC2 = AB2 + BE2 + 2 AB × BE + CE2  → (1)

From the figure CD = EF (Since CDFE is a rectangle)

But CD= AB

⇒ AB = CD = EF

Also CE = DF (Distance between two parallel lines)

ΔAFD ≅ ΔBEC (RHS congruence rule)

⇒ AF = BE

Consider right angled ΔDFB

BD2 = BF2 + DF2 [By Pythagoras theorem]

        = (EF – BE)2 + CE2  [Since DF = CE]

        = (AB – BE)2 + CE2   [Since EF = AB]

 ⇒ BD2 = AB2 + BE2 – 2 AB × BE + CE2  → (2)

Add (1) and (2), we get

AC2 + BD2 = (AB2 + BE2 + 2 AB × BE + CE2) + (AB2 + BE2 – 2 AB × BE + CE2)

                     = 2AB2 + 2BE2 + 2CE2

  AC2 + BD2 = 2AB2 + 2(BE2 + CE2)  → (3)

From right angled ΔBEC, BC2 = BE2 + CE2 [By Pythagoras theorem]

Hence equation (3) becomes,

  AC2 + BD2 = 2AB2 + 2BC2

                                  = AB2 + AB2 + BC2 + BC2

                                  = AB2 + CD2 + BC2 + AD2

∴   AC2 + BD2 = AB2 + BC2 + CD2 + AD2

Thus the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

(1/7)^-3

=7^3

=343

Only u have express the power in negative

2500

1296

Step-by-step explanation:

2500=2*2*5*5*5*7

1296=2*2*2*2*3*3*3*3

6.25 = 625*10^-2

97.9925 = 979925*10^-4

85.0000 = 85

00.899 = 899*10^-3

66.503 = 66503*10-3

8^-1 or 2^-3

Step-by-step explanation:

⅛ = 8^-1 = 2^-3.

Since, from laws of exponents we have,

x^-1 = 1/x, it implies that we may write

⅛ = 8^-1

Alternatively, we may also use prime factorization to write it as,

⅛ = 1/2³= 2^-3

Hope it helps :)

a × a × a × 3 × 3 × 3 = a^3 × 3^3 .

answer  (2/5)^5

Step-by-step explanation: 32 =2^5 and 243=3^5

please mark as brainliest

a^3 × 3^3

Step-by-step explanation:a×a×a = a^3

3×3×3 = 3^3