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- Question
- Simplify ( 6a-2bc-3/4ab-3c2 ) ÷ ( 5a-3 b2c-1/3ab-2c3 )
Options- A. 9/10ac
- B. 9/10ac-1
- C. 9/10ac2
- D. 9/10ac-3
- Correct Answer
- 9/10ac-1
ExplanationGiven equation is,
( 6a-2bc-3/4ab-3c2 ) ÷ ( 5a-3 b2c-1/3ab-2c3 )
Apply the algebra law a ÷ b = a x 1/b
= ( 6a-2bc-3/4ab-3c2 ) x ( 3ab-2c3/5a-3 b2c-1 )
= ( 6a-2 bc-3 x 3ab-2c3) / ( 4ab-3c2 x 5a-3b2c-1 )
Apply the law of Fractional Exponents and Laws of Exponents
(am)(an) = am+n
am÷an=am-n
Or
am/an=am-n
= 18a-2 + 1 b1 - 2 c -3 + 3 / 20a1 - 3 b-3 + 2 c2 - 1
= 9a-1b-1c0/ 10a - 2 b-1c1
= ( 9/10 ) a-1 + 2b-1 + 1 c0 - 1
= ( 9/10 ) a1b0 c-1
= ( 9/10 ) ac-1 [? b0 = 1] - 1. The expression [(?2)?2]?2 gives
Options- A. a natural number
- B. a integer and not a natural number
- C. a rational number but not an integer.
- D. a real number but not a rational number Discuss
- 2. If ( 5 + 2?3 ) / ( 7 + 4?3 ) = a + b?3, then the value of a and b is?
Options- A. a = 11, b = -6
- B. a = 6, b = 11
- C. a = -11, b = 6
- D. a = -11, b = -6 Discuss
- 3. ?5 + ?x = 3, then the value of x is?
Options- A. 64
- B. 125
- C. 9
- D. 27 Discuss
- 4. 812.5 x 94.5 ÷ 34.8 = 9?
Options- A. 7.1
- B. 9.4
- C. 4.7
- D. 4.5 Discuss
- 5. ( 42 x 229 ) ÷ ( 9261)1/3 =?
Options- A. 448
- B. 452
- C. 456
- D. 458 Discuss
- 6. The value of 273 × 34 ÷ 310 is equal to :
Options- A. 9
- B. 27
- C. 81
- D. 1 27 Discuss
- 7.
The expression ( - 1 ) 132 is equivalent to : 5- 1 + 3- 1
Options- A. 16 9
- B. - 15 8
- C. 15 8
- D. 17 8 Discuss
- 8.
The value of ( - 1 ) -(2/3) 125
Options- A. 1 25
- B. 25
- C. 5
- D. 1 5 Discuss
- 9. The value of ( 8 ) - ( 2 - 2 ) is :
Options- A. - 1 2 4
- B. - 3 2 4
- C. 3 2 4
- D. - 1 2 2 Discuss
- 10. If 102/5 × 108/5 = 10n, the value of n is :
Options- A. 2
- B. 3
- C. 6
- D. 4 Discuss
Surds and Indices problems
Search Results
Correct Answer: a real number but not a rational number
Explanation:
Given expression = [(?2)?2]?2
= (?2)(2)?2/2
= (?2)(2)1/?2
= (2)1/2 x 21/?2
= 2(2/21/?2)
= (2)(2)(1/?2 - 1)
which denotes a real number but not a rational number .
Correct Answer: a = 11, b = -6
Explanation:
Given equation is,
( 5 + 2?3 ) / (7 + 4?3 )
Now Multiply and divide by ( 7 - 4?3 ) in above given equation.
By Rationalization, we will get,
[ ( 5 + 2?3 ) / ( 7 + 4?3 ) ] x [ ( 7 - 4?3 ) / ( 7 - 4?3 ) ]
[ ( 5 + 2?3 ) x ( 7 - 4?3 ) ] / [ ( 7 + 4?3 ) x ( 7 - 4?3 ) ]
Apply the formula and multiplication rule of algebra,
( P + Q ) x (R - S ) = P x R - P x S + Q x R - Q x S .................(1)
( a + b ) x ( a - b) = a2 - b2.......................................................(2)
= ( 5 x 7 - 5 x 4?3 + 7 x 2?3 - 2?3 x 4?3 )/ ( 72 - (4?3)2 )
= 35 - 20?3 + 14?3 - 8 x 3 / ( 49 - 16 x 3 )
= ( 35 - 24 - 6?3 )/(49 - 48 )
= 11 - 6?3
? ( 5 + 2?3 ) /( 7 + 4?3 ) = a + b?3
? a + b?3 = 11 - 6?3
on equating the above equation and we get,
or a = 11 and b = - 6
Correct Answer: 64
Explanation:
?5 + ?x = 3
Apply the law of Algebra Law.
Square both side of equation.
(?5 + ?x)2 = 32
? 5 + ?x = 9
? ?x = 9 - 5
? ?x = 4
Now cube the both side of equation,
? ( ?x ) 3 = 43
? x = (4)3
? x = 64
Correct Answer: 7.1
Explanation:
812.5 X 94.5 ÷ 34.8 = 9?
? 812.5 x 94.5 ÷ 34.8 = 9?
Apply the law of Fractional Exponents and Laws of Exponents
(am)n = am x n ----------------1
(am) x (an) = am + n-------------2
am ÷ an = am ? n----------------3
and if pX = pY then X will be equal to Y. means X = Y;----------------4
Apply Law 1
? (92)2.5 x 94.5 ÷ 32 x 2.4 = 9?
? 95 x 94.5 ÷ 92.4 = 9?
Apply law 2 and 3,
? 9(5 + 4.5 - 2.4) = 9?
? 9? = 97.1
Apply the Law 4
? ? = 7.1
Correct Answer: 458
Explanation:
Given that, (42 x 229) ÷ (9261)1/3 = ?
As we know that (9621)1/3 = (21 x 21 x 21)1/3 = 213x1/3
? 42 x 229 ÷ (213 x )1/3 = ?
? 42 x 229 ÷ 21 = ?
? 42 x 229 x 1/ 21 = ?
? 2 x 229 = ?
? ? = 2 x 229
? ? = 458
Correct Answer: 27
Explanation:
Correct Answer: 15 8
Explanation:
Correct Answer: 25
Correct Answer: - 3 2 4
Explanation:
Correct Answer: 2
Explanation:
? 102/5 × 108/5 = 10n
? 102/5 + 8/5 = 10n
? 1010/5 = 10n ? 102 = 10n ? n = 2
Hence, the value of n is 2.
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