Evaluate 625^(-3/4)

Problem

625^(−3/4)

Solution

1. Rewrite the expression using the property of negative exponents, a^(−n)=1/(a^n)

1/(625^(3/4))

2. Apply the definition of rational exponents, a^(m/n)=(√(n,a))^m

1/((√(4,625))^3)

3. Evaluate the fourth root of 625 by recognizing that 5^4=625

√(4,625)=5

4. Substitute the root back into the expression and calculate the power.

1/5^3

5. Simplify the denominator by calculating 5×5×5

1/125

Final Answer

625^(−3/4)=1/125

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