(16)^?3/4 + 2^?3 + (8)^?2/3 is equivalent to :

Correct Answer: 3a b 2 c

Explanation:

Correct Answer: 1

Explanation:

If any given number (suppose x) is a rational number other than zero, then x⁰ = 1.

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: 32 a6

Explanation:

Correct Answer: 9

Explanation:

Correct Answer: 1

Explanation:

Correct Answer: 27

Explanation:

? 3^x - 3^{x - 1} = 18
? 3^{x - 1}(3 - 1) = 18
? 3^{x - 1}(2) = 18
? 3^{x - 1} = 18/2
? 3^{x - 1} = 9
? 3^{x - 1} = 3²
Apply the Algebra law,
If a^X = a^Y then X will be equal to Y.
means X = Y;
? x - 1 = 2
? x = 3
Then x^x = (3)³ = 27

Correct Answer: - 1

Explanation:

Given that, a^{2x + 2} = 1
Apply the algebra Law,
p⁰ = 1
? a^{2x + 2} = a⁰
Apply the algebra law
p^X = p^Y then X will be equal to Y. means X = Y;
? 2x + 2 = 0
? x = -2/2 = -1