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
- 163/2 + 16 -3/2 = ?
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163/2 + 16-3/2
Apply the law of Fractional Exponents and Laws of Exponents
am x an = am+n
a-m = 1/am
⇒163/2 + 1/163/2Correct Option: B
163/2 + 16-3/2
Apply the law of Fractional Exponents and Laws of Exponents
am x an = am+n
a-m = 1/am
⇒163/2 + 1/163/2
⇒(161/2)3 + 1/(161/2)3
⇒(42 x 1/2)3 + 1/(42 x 1/2)3
⇒43 + 1/43
⇒ 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,
(am)n = amnCorrect Option: D
? = [(12)-2]2/[(12)2]-2
Apply the Algebra Law,
(am)n = amn
= (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
(am) x (an) = am + n-------------------1
am ÷ an = am ? n----------------2Correct Option: B
Given that ,(16)9 ÷ (16)4 x (16) 3 = (16)?
Apply the law of Fractional Exponents and Laws of Exponents
(am) x (an) = am + n-------------------1
am ÷ an = am ? 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 1/43
? = [ 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