? = ∛103823
? = ∛(47) ³
Apply the Law of Algebra

Correct Option: D

? = ∛103823
? = ∛(47) ³
Apply the Law of Algebra
? = [(47)³]^1/3
? = 47^{3 x 1/3} = 47
? = 47

? = [ (11)³ x (6)² ] x 1/4³
? = [ 11³ x 6² ] x 1/4³
Solve the equation by algebra law.

Correct Option: B

? = [ (11)³ x (6)² ] x 1/4³
? = [ 11³ x 6² ] x 1/4³
Solve the equation by algebra law.
?= [ 1331 x 36 ] x 1/64 =1331 x 36 / 64
? = 748.6875

Given that , (16)⁹ ÷ (16)⁴ x (16) ³ = (16)^?

Apply the law of Fractional Exponents and Laws of Exponents
(a^m) x (aⁿ) = a^{m + n}-------------------1
a^m ÷ aⁿ = a^{m ? n}----------------2

Correct Option: B

Given that ,(16)⁹ ÷ (16)⁴ x (16) ³ = (16)^?
Apply the law of Fractional Exponents and Laws of Exponents
(a^m) x (aⁿ) = a^{m + n}-------------------1
a^m ÷ aⁿ = a^{m ? n}----------------2
⇒ (16)⁹ ÷ (16)⁴ x (16) ³ = (16)^?
⇒ (16)^? = (16)^{9 + 3 - 4}
⇒ ? = 12 - 4 = 8

? = [(12)^-2]²/[(12)²]^-2
Apply the Algebra Law,
(a^m)ⁿ = a^mn

Correct Option: D

? = [(12)^-2]²/[(12)²]^-2
Apply the Algebra Law,
(a^m)ⁿ = a^mn
= (12) ^{- 4}/(12) ^{- 4}
= 1

16^3/2 + 16^-3/2
Apply the law of Fractional Exponents and Laws of Exponents
a^m x aⁿ = a^m+n
a^-m = 1/a^m
⇒16^3/2 + 1/16^3/2

Correct Option: B

16^3/2 + 16^-3/2
Apply the law of Fractional Exponents and Laws of Exponents
a^m x aⁿ = a^m+n
a^-m = 1/a^m
⇒16^3/2 + 1/16^3/2
⇒(16^1/2)³ + 1/(16^1/2)³
⇒(4^{2 x 1/2})³ + 1/(4^{2 x 1/2})³
⇒4³ + 1/4³
⇒ 64 + 1/64
⇒ (64 x 64+ 1)/64
= (4096+1)/64
= 4097/64