Test: Exponents and Powers

4*4*4*4 = 256

256 = 4⁴

So option B is the correct answer. 

So option C is the correct answer. 

 2048 = 2 x 1024

= 2 x 2 x 512

= 2 x 2 x 2 x 256

= 2 x 2 x 2 x 2x 128

= 2 x 2 x 2 x 2 x 2 x 64

= 2 x 2 x 2 x 2 x 2 x 2 x 32

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 16

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 8

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 2¹¹

So option B is the correct answer. 

Prime factorization of 432 is,

432 =2×2×2×2×3×3×3

to express this as power

432=(2)^⁴×(3)^³

If any power having a odd number is raised to -1 then result will be -1

So (−1)⁵⁵ = -1

So option B is correct answer. 

If any power having a even number is raised to -1 then the  result will be 1

Since the power is an even number , So (−1)⁵⁰⁰ =  1 

If any power having a odd number is raised to -1 then result will be -1

So (−1)⁴⁷ = -1

So option A is correct answer. 

If any power having an even number is raised to -1 then the  result will be 1

Since the power is an even number , So (−1)⁴⁰⁰ =  1 

So option A is the correct answer. 

Points by which Anu fell short is

= 26 - 8/3 = (78 - 8)/3

= 70/3

25⁴/5³ = (5²)^4/5³=5⁸/5³=5^8-3=5⁵

 a × a × a × c × c × c × c × d = a³ × c⁴ × d

512=8*8*8=8³=(2³)³=2^3*3=2⁹

Anything raised to the power zero is 1 . 

(-2)³(-10)³=(-2)*(-2)*(-2)*(-10)*(-10)*(-10), which is the expansion of the exponential forms which means the power depicts how many times a number is multiplied.

Exponents, or powers, are a way of indicating that a quantity is to be multiplied by itself some number of times. In the expression 2⁵, 2 is called the base and 5 is called the exponent, or power.

Anything raised to the power zero is 1 .

In the given expression,  (4⁰ - 2⁰) x 5⁰

                                             = (1 - 1) x 1

                                      = ( 0 ) x 1

                                      = 0

So Option B is correct answer. 

Given, a = 3 and b = 4 

a^a + b^b = 3³ + 4⁴ = 3 x 3 x 3 + 4 x 4 x 4 x 4

                            = 27 + 16 x 16 

                            = 27 + 256

                            = 283

So option A is the correct answer. 

Whenever you multiply two terms with the same base, you can add the exponents:

( x ^m ) ( x ⁿ ) = x^{( m + n )}

So (2/7)² x (2/7)⁴  = (2/7)⁶

So option C is the correct answer. 

1 lakh is equal to 10⁵ 

So option A is the correct answer.