(100)⁰ is equivalent to :

Correct Answer: 12

Explanation:

?2ⁿ = 64 ? 2ⁿ = (64)²
? 2ⁿ = (2 × 2 × 2 × 2 × 2 × 2)²
? 2ⁿ = (26)² ? 2ⁿ = 26 × 2 = 212
? n = 12.

Correct Answer: 4

Explanation:

Given that ,
m = 7 - 4?3
Then I/m = 1/7 - 4?3......................(1)

Now multiply and divide with 7 + 4?3 in Eq. (1)
We will get,
1/m = ( 1/7 - 4?3 ) x ( 7 + 4?3 / 7 + 4?3)
?1/m = ( 7 + 4?3 )/ ( 7 - 4?3 ) x ( 7 + 4?3
?1/m = ( 7 + 4?3 ) / ( 7² - ( 4?3)² )
?1/m = ( 7 + 4?3 ) / ( 49 - 4 x 4 x 3 )
?1/m = ( 7 + 4?3 ) /49 - 48
?1/m = ( 7 + 4?3 ) / 1
?1/m = 7 + 4?3
? m + 1/m = 14
? ( m + 1/m ) + 2 = 14 + 2 = 16
? (?m + 1/?m)² = ( m + 1/m )+ 2
? (?m + 1/?m)² = 16
? (?m + 1/?m)² = 4²
? (?m + 1/?m) = 4

Correct Answer: irrational unless n is the mth power of an integer

Explanation:

If m and n are natural numbers, then m?n is irrational unless n is m^th power of an integer.

Correct Answer: 14

Explanation:

Given that, a = 2 + ? 3
Then, 1/a = 2 - ?3 [ by conjugate property ]
Conjugate law is below,
if x = p + ? q
then 1/x = p - ? q
Apply the law of algebra in above equation.
Now, we have, a ² + a ^-2
= ( a + 1/a ) ² - 2
= ( 2 + ? 3 + 2 - ? 3) ² - 2
= (4) ² - 2 = 16 - 2 = 14

Correct Answer: 1

Explanation:

? = 1/ ( 1 + x^{b - a} + x^{c - a} ) + 1/ ( 1 + x^{a - b} + x^{c - b} ) + 1 / ( 1 + x^{b - c} + x^{a - c} )
Apply the law of algebra and solve the given equation.
? ? =1/ ( 1 + x^b/x^a + x^c/x^a ) + 1/ ( 1+ x^a/x^b + x^c/x^b ) + 1/ ( 1 + x^b/x^c + x^a/x^c )
? ? = x^a/ ( x^a+x^b+x^c ) + x^b/ ( x^b + x^a+ x^c ) + x^c/ ( x^c+x^b+x^a )
? ? = ( x^a + x^b + x^c ) / ( x^a + x^b + x^c ) = 1

Correct Answer: 3a b 2 c

Explanation:

Correct Answer: 1 2

Explanation:

Correct Answer: 32 a6

Explanation:

Correct Answer: 9

Explanation:

Correct Answer: 1

Explanation: