8^12*64^a*40^24*25^13=40^5
Answers
Answer:
a = 7
Step-by-step explanation:
Correct Question Would be
8¹² * 64ᵃ * 40²⁴ * 25¹³ = 40⁵⁰
Concept used :
(ab)ⁿ = aⁿ * bⁿ
(aᵇ)ⁿ = aᵇⁿ
aᵇ * aⁿ = a⁽ᵇ⁺ⁿ⁾
8¹² * 64ᵃ * 40²⁴ * 25¹³ = 40⁵⁰
=> (2³)¹² * (2⁶)ᵃ * (2³ * 5)²⁴ * (5²)¹³ = ( 2³ * 5)⁵⁰
=> 2³ˣ¹² * 2⁶ᵃ * (2³)²⁴ * (5)²⁴ * 5²ˣ¹³ = ( 2³)⁵⁰ * 5⁵⁰
=> 2³⁶ * 2⁶ᵃ * 2⁷² * 5²⁴ * 5²⁶ = 2³ˣ⁵⁰ * 5⁵⁰
=> 2⁽³⁶ ⁺⁶ᵃ ⁺ ⁷²⁾ * 5⁽²⁴ ⁺²⁶⁾ = 2¹⁵⁰ * 5⁵⁰
=> 2⁽³⁶ ⁺⁶ᵃ ⁺ ⁷²⁾ * 5⁵⁰ = 2¹⁵⁰ * 5⁵⁰
cancelling 5⁵⁰ from both sides
=> 2⁽³⁶ ⁺⁶ᵃ ⁺ ⁷²⁾ = 2¹⁵⁰
Equating Powers
=> 36 + 6a + 72 = 150
=> 6a = 42
=> a = 7
Answer:
a = 7
Step-by-step explanation:
Correct Question Would be
8¹² * 64ᵃ * 40²⁴ * 25¹³ = 40⁵⁰
Concept used :
(ab)ⁿ = aⁿ * bⁿ
(aᵇ)ⁿ = aᵇⁿ
aᵇ * aⁿ = a⁽ᵇ⁺ⁿ⁾
8¹² * 64ᵃ * 40²⁴ * 25¹³ = 40⁵⁰
=> (2³)¹² * (2⁶)ᵃ * (2³ * 5)²⁴ * (5²)¹³ = ( 2³ * 5)⁵⁰
=> 2³ˣ¹² * 2⁶ᵃ * (2³)²⁴ * (5)²⁴ * 5²ˣ¹³ = ( 2³)⁵⁰ * 5⁵⁰
=> 2³⁶ * 2⁶ᵃ * 2⁷² * 5²⁴ * 5²⁶ = 2³ˣ⁵⁰ * 5⁵⁰
=> 2⁽³⁶ ⁺⁶ᵃ ⁺ ⁷²⁾ * 5⁽²⁴ ⁺²⁶⁾ = 2¹⁵⁰ * 5⁵⁰
=> 2⁽³⁶ ⁺⁶ᵃ ⁺ ⁷²⁾ * 5⁵⁰ = 2¹⁵⁰ * 5⁵⁰
cancelling 5⁵⁰ from both sides
=> 2⁽³⁶ ⁺⁶ᵃ ⁺ ⁷²⁾ = 2¹⁵⁰
Equating Powers
=> 36 + 6a + 72 = 150
=> 6a = 42
=> a = 7