Evaluate 3^-5

Problem

3(−5)

Solution

1. Identify the negative exponent rule, which states that a(−n)=1/(an) for any non-zero base a

2. Rewrite the expression by moving the base to the denominator and changing the sign of the exponent.

3(−5)=1/3

3. Calculate the value of the power in the denominator by multiplying the base by itself 5 times.

3×3×3×3×3=243

4. Substitute the calculated value back into the fraction.

1/3=1/243

Final Answer

3(−5)=1/243

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