Evaluate 24/(((5)^2+24)^(3/2))

Problem

24/((5^2+24)^(3/2))

Solution

1. Evaluate the exponent inside the parentheses by calculating 5^2

5^2=25

2. Add the terms inside the parentheses.

25+24=49

3. Substitute the sum back into the expression.

24/(49^(3/2))

4. Apply the definition of a rational exponent, where a^(3/2)=(√(,a))^3

49^(3/2)=(√(,49))^3

5. Calculate the square root of 49.

√(,49)=7

6. Evaluate the cube of the result.

7^3=343

7. Simplify the final fraction.

24/343

Final Answer

24/((5^2+24)^(3/2))=24/343

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