(0.49)⁴ x (0.343)⁴ ÷ (0.2401)⁴ x = (70 ÷ 100)^{? + 3} ?

The given question is,
(70 ÷ 100)^{? + 3} = (0.49)⁴ x (0.343)⁴ ÷ (0.2401)⁴
As we know that
70 ÷ 100 = 0.7
0.49 = 0.7 ²
0.343 = 0.7 ³
0.2401 = 0.7 ⁴
Put these value in given question , we will get
? (0.7)^{? + 3} = (0.7²)⁴ x ( 0.7³ )⁴ ÷ ( 0.7⁴ )⁴
? (0.7) ^{? + 3} = 0.7 ^{2 x 4} x 0.7 ^{3 x 4} ÷ 0.7 ^{4 x 4}
? (0.7) ^{? + 3} = 0.7 ⁸ x 0.7 ¹² ÷ 0.7 ¹⁶
Apply the law of Fractional Exponents and Laws of Exponents
(a^m)(aⁿ) = a^m+n
a^m÷aⁿ=a^m-n
Or
a^m/aⁿ=a^{m - n}
we will get,
? (0.7)^{? + 3} = (0.7) ^{8 + 12 - 16}
? (0.7)^{? + 3} = (0.7) ^{20 - 16}
? (0.7)^{? + 3} = (0.7) ⁴
On comparing the exponents both sides, we get
? + 3 = 4
? ? = 4 - 3 = 1