9x^(5/2) - 7x^(3/2) at x = 4
Solution 1
To evaluate the expression 9x^(5/2) - 7x^(3/2) at x = 4, we need to substitute x with 4 in the expression and simplify.
Step 1: Substitute x with 4 in the expression: 9(4)^(5/2) - 7(4)^(3/2)
Step 2: Simplify the exponents: 9(4^(5/2)) - 7(4^(3/2))
Step 3: Evaluate the exponent: 4^(5/2) = (4^2)^(5/2) = 16^(5/2) = 256
4^(3/2) = (4^2)^(3/2) = 16^(3/2) = 64
Step 4: Substitute the evaluated exponents back into the expression: 9(256) - 7(64)
Step 5: Perform the multiplication: 2304 - 448
Step 6: Perform the subtraction: 1856
Therefore, the value of the expression 9x^(5/2) - 7x^(3/2) at x = 4 is 1856.
Solution 2
To evaluate the expression 9x^(5/2) - 7x^(3/2) at x = 4, we need to substitute x with 4 in the expression and simplify.
Step 1: Substitute x with 4 in the expression: 9(4)^(5/2) - 7(4)^(3/2)
Step 2: Simplify the exponents: 9(4^(5/2)) - 7(4^(3/2))
Step 3: Evaluate the exponent: 4^(5/2) = (4^2)^(5/2) = 16^(5/2) = 256
4^(3/2) = (4^2)^(3/2) = 16^(3/2) = 64
Step 4: Substitute the evaluated exponents back into the expression: 9(256) - 7(64)
Step 5: Perform the multiplication: 2304 - 448
Step 6: Perform the subtraction: 1856
Therefore, the value of the expression 9x^(5/2) - 7x^(3/2) at x = 4 is 1856.
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