(25)^{7.5} × (5)^{2.5} ÷ (125)^{1.5} equals 5 raised to which power?

Given data & idea

• Rewrite all bases as powers of 5: 25 = 5^2, 125 = 5^3.
• Use (a^m)^n = a^{mn} and combine exponents.

Step-by-step calculation

(25)^{7.5} = (5^2)^{7.5} = 5^{15}(5)^{2.5} = 5^{2.5}(125)^{1.5} = (5^3)^{1.5} = 5^{4.5}Overall exponent = 15 + 2.5 − 4.5 = 13.

Verification

Result = 5^{13} ⇒ power is 13.

Common pitfalls

• Mistakenly adding denominators instead of subtracting exponents for division.

Final Answer

Power = 13.