(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?

Solution:

• Write the expression with explicit exponents: 25^(7.5) × 5^(2.5) ÷ 125^(1.5).

• Convert bases to powers of 5: 25 = 5^2 and 125 = 5^3. So the expression becomes (5^2)^(7.5) × 5^(2.5) ÷ (5^3)^(1.5).

• Use (a^b)^c = a^(b·c): (5^2)^(7.5) = 5^(2·7.5) = 5^15 and (5^3)^(1.5) = 5^(3·1.5) = 5^4.5. Now we have 5^15 × 5^2.5 ÷ 5^4.5.

• Combine exponents (multiply ⇒ add exponents; divide ⇒ subtract exponents): 5^(15 + 2.5 − 4.5) = 5^13.

• Therefore the expression equals 5^13, so the exponent value is 13.