## Surds and Indices

1. Solve the below equation and find the value of ?.

(13)4 = ?
1. 520
2. 169
3. 28561
4. 14280
1. ? = √(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

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1. 163/2 + 16 -3/2 = ?
1. 0
2. 4097/64
3. 1
4. 16/9097
1. 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

##### Correct 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

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1. [(12)-2]2/[(12)2]-2 = ?
1. 12
2. 4.8
3. 12/144
4. 1
1. ? = [(12)-2]2/[(12)2]-2
Apply the Algebra Law,
(am)n = amn

##### Correct Option: D

? = [(12)-2]2/[(12)2]-2
Apply the Algebra Law,
(am)n = amn

= (12) - 4/(12) - 4
= 1

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1. (16)9 ÷ (16)4 x (16)3 = (16)?
1. 6.75
2. 8
3. 10
4. 12
1. 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

##### Correct 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

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1. [ (11)3 x (6)2] ÷ (4)3 = ?
1. 2994.75
2. 748.6875
3. 272.25
4. 4492.125
1. ? = [ (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

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