Value of ? in expression 78.9 ÷ (343)1.7 x (49)4.8

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Value of ? in expression
7^8.9 ÷ (343)^1.7 x (49)^4.8 = 7^? is

1. 13.4
2. 12.8
3. 11.4
4. 9.6
5. None of the above

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