Given that
(0.00032)^2/5 = (32/100000)^2/5
Solve the equation by algebra Law

Correct Option: D

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

Given that, (2^{4x 1/2})^? = 256
Apply the law of Fractional Exponents and Laws of Exponents
(a^m)ⁿ = a^{m x n} ----------------1
(a^m) x (aⁿ) = a^{m + n}-------------------2
a^m ÷ aⁿ = a^{m ? n}----------------3
and if p^X = p^Y then X will be equal to Y. means X = Y;----------------4

Correct Option: C

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

Given, √10 + ∛ x = 4
On squaring both sides,
After squaring the both sides,
Now, cubic on both sides,
Then solve the equation.

Correct Option: B

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

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

Correct Option: A

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

Given that, a^{2x + 2} = 1
Apply the algebra Law,
p⁰ = 1
and if
p^X = p^Y
then X will be equal to Y. means X = Y;

Correct Option: B

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