If 2^{x - 1} + 2^{x + 1} = 2560, find the value of x.

Correct Answer: 1/25

Explanation:

Given that
(0.00032)^2/5 = (32/100000)^2/5
Solve the equation by algebra Law
= (2⁵/10⁵)^2/5
= {(2/10)⁵}^2/5
= (2/10)^5x2/5
= (1/5)² = 1/25

Correct Answer: 4

Explanation:

Given that, (2^{4x 1/2})^? = 256
Apply the law of Fractional Exponents and Laws of Exponents
? (2²)^? = 2⁸
? 2^{2 x ?} = 2⁸
? 2 x ? = 8
? ? = 8/2 = 4

Correct Answer: 216

Explanation:

Given, ?10 + ? x = 4
On squaring both sides, we get
10 + ?x = 16
? ?x = 6
Now, cubic on both sides, we get
x = (6)³ = 216

Correct Answer: 13.4

Explanation:

7^8.9 ÷ (343)^1.7 x (49)^4.8 = 7^?
Apply the law of Fractional Exponents and Laws of Exponents
(a^m)(aⁿ) = a^m+n
a^m÷aⁿ=a^m?n
a^m/aⁿ=a^m?n
(a^m)ⁿ = a^mn
7^8.9 ÷ (343)^1.7 x (49)^4.8 = 7^?
? 7^8.9 ÷ (7³)^1.7 x (7²)^4.8 = 7^?
? 7^8.9 ÷ 7^5.1 x 7^9.6 = 7^?
? 7^{8.9 - 5.1 + 9.6} = 7^?
? 7^{18.5 - 5.1} = 7^?
? ? = 13.4

Correct Answer: - 1

Explanation:

Given that, a^{2x + 2} = 1
Apply the algebra Law,
p⁰ = 1
? a^{2x + 2} = a⁰
Apply the algebra law
p^X = p^Y then X will be equal to Y. means X = Y;
? 2x + 2 = 0
? x = -2/2 = -1

Correct Answer: 10000

Explanation:

Given equation is
(10)²⁰⁰ ÷ (10)¹⁹⁶
Apply the law of Algebra
a^m ÷ aⁿ = a^{m ? n}
= (10)^{200 - 196}
= 10⁴
= 10000

Correct Answer: 0

Explanation:

?5 + 2?6 - 1/?5 - 2?6
= ((?5 + 2?6 x ?5 - 2?6 ) - 1)/?5 - 2?6

Apply the formula of Algebra.
( a + b ) x (a - b ) = a² - b²
= (?(5)² - (2?6 )² - 1)/?5 - 2?6
= (?25 - 4 x 6 - 1) /?5 - 2?6
= (?25 - 24 - 1) /?5 - 2?6
= (? 1 - 1 )/?5 - 2?6
= (1 - 1 )/?5 - 2?6
= 0/?5 - 2?6
= 0

Correct Answer: 7

Explanation:

? 2^{x - 1} + 2^{x + 1} = 320
Apply the law of Algebra
? 2^{x - 1}(1 + 2 ² ) = 320
? 2^{x - 1}(1 + 4 ) = 320
? 2^{x - 1} x 5 = 320
? 2^{x - 1} = 64 = 2 x 2 x 2 x 2 x 2 x 2
? 2^{x - 1} = 2⁶
if p^X = p^Y then X will be equal to Y. means X = Y;
? x - 1 = 6
? x = 7

Correct Answer: a

Explanation:

Given, xyz = 1, a^x = b, b^y = c
Now, b = a^x
Apply the law of algebra .
Take the power y of both side equation.
? b^y= a^xy
Take the power z of both side equation.
? b^yz = a^xyz
? ( b^y )^z = a^xyz
Replace the b^y with c and xyz with 1 as per given equation,
? c^z = a

Correct Answer: 3n + 10

Explanation:

Given that 16 x 8^{n + 2} = 2^m

Apply the law of Fractional Exponents and Laws of Exponents
if a multiply three times a x a x a then
a x a x a = a³
if a multiply two times a x a then
a x a = a²
if a multiply n times a x a x a x....up to n times, then
a x a x a x a ......up to n times = aⁿ
? (2)⁴ x 2^{3 x (n+2)} = 2^m
? (2)⁴ x 2³ⁿ⁺⁶ = 2^m
a^maⁿ = a^m+n
? (2)^{(4 + 3n + 6)} = 2^m
? (2)^{(3n + 10)} = 2^m
if p^X = p^Y then X will be equal to Y. means X = Y;
On comparing, we get
3n + 10 = m
? m = 3n + 10;