Surds and Indices
 Solve the below equation and find the value of ?.
√(13)^{4} = ?

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? = √(13)^{4} = √13 x 13 x 13 x 13
Apply the rule of square root.Correct Option: B
? = √(13)^{4} = √13 x 13 x 13 x 13
Apply the rule of square root.
= 13 x 13 = 169
 16^{3/2} + 16 ^{ 3/2} = ?

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16^{3/2} + 16^{3/2}
Apply the law of Fractional Exponents and Laws of Exponents
a^{m} x a^{n} = 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 a^{n} = 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}
⇒4^{3} + 1/4^{3}
⇒ 64 + 1/64
⇒ (64 x 64+ 1)/64
= (4096+1)/64
= 4097/64
 [(12)^{2}]^{2}/[(12)^{2}]^{2} = ?

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? = [(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)^{9} ÷ (16)^{4} x (16)^{3} = (16)^{?}

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Given that , (16)^{9} ÷ (16)^{4} x (16) ^{3} = (16)^{?}
Apply the law of Fractional Exponents and Laws of Exponents
(a^{m}) x (a^{n}) = a^{m + n}1
a^{m} ÷ a^{n} = a^{m ? n}2Correct 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 (a^{n}) = a^{m + n}1
a^{m} ÷ a^{n} = a^{m ? n}2
⇒ (16)^{9} ÷ (16)^{4} x (16) ^{3} = (16)^{?}
⇒ (16)^{?} = (16)^{9 + 3  4}
⇒ ? = 12  4 = 8
 [ (11)^{3} x (6)^{2}] ÷ (4)^{3} = ?

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? = [ (11)^{3} x (6)^{2} ] x 1/4^{3}
? = [ 11^{3} x 6^{2} ] x 1/4^{3}
Solve the equation by algebra law.Correct Option: B
? = [ (11)^{3} x (6)^{2} ] x 1/4^{3}
? = [ 11^{3} x 6^{2} ] x 1/4^{3}
Solve the equation by algebra law.
?= [ 1331 x 36 ] x 1/64 =1331 x 36 / 64
? = 748.6875