Evaluate (3^-2+4^-2)^(-1/2)

Problem

(3(−2)+4(−2))(−1/2)

Solution

1. Rewrite the negative exponents inside the parentheses as fractions using the rule a(−n)=1/(an)

3(−2)=1/3

4(−2)=1/4

2. Calculate the squares of the denominators.

1/3=1/9

1/4=1/16

3. Find a common denominator to add the fractions inside the parentheses.

1/9+1/16=16/144+9/144

(16+9)/144=25/144

4. Apply the negative exponent rule to the entire expression, which flips the fraction.

(25/144)(−1/2)=(144/25)(1/2)

5. Evaluate the square root, as the exponent 1/2 represents the square root of the fraction.

√(,144/25)=√(,144)/√(,25)

12/5

6. Convert to a decimal if necessary.

12/5=2.4

Final Answer

(3(−2)+4(−2))(−1/2)=12/5

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