Evaluate 625^(-3/4)

Problem

625(−3/4)

Solution

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

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=625

√(4,625)=5

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

1/5

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

1/125

Final Answer

625(−3/4)=1/125

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