Use a scientific calculator to evaluate (a) \(10^{1.2}\) (b) \(6^{-0.7}\) (c) \(6^{2.5}\) (d) \(\left(3^{-1} 4^{2}\right)^{0.8}\)

Short Answer

Expert verified
Question: Calculate the values of the following expressions using a scientific calculator: a) \(10^{1.2}\) b) \(6^{-0.7}\) c) \(6^{2.5}\) d) \(\left(3^{-1} 4^{2}\right)^{0.8}\) Answer: a) \(10^{1.2} \approx 15.8489\) b) \(6^{-0.7} \approx 0.2154\) c) \(6^{2.5} \approx 233.0478\) d) \(\left(3^{-1} 4^{2}\right)^{0.8} \approx 4.2162\)

Step by step solution

01

(Step 1: Prepare your scientific calculator)

Make sure your scientific calculator is turned on, functional, and set to the correct mode (if applicable) for calculating powers.
02

(Step 2: Evaluate \(10^{1.2}\))

Enter "10" into your calculator followed by the "^" button (or its equivalent) and then enter "1.2". Press "=" or "Enter" to get the result. The value should be approximately 15.8489.
03

(Step 3: Evaluate \(6^{-0.7}\))

Clear the calculator and enter "6" followed by the "^" button (or its equivalent) and then enter "-0.7". Press "=" or "Enter" to get the result. The value should be approximately 0.2154.
04

(Step 4: Evaluate \(6^{2.5}\))

Clear the calculator and enter "6" followed by the "^" button (or its equivalent) and then enter "2.5". Press "=" or "Enter" to get the result. The value should be approximately 233.0478.
05

(Step 5: Evaluate \(\left(3^{-1} 4^{2}\right)^{0.8}\))

First, we need to simplify the expression inside the parentheses. Clear the calculator and enter "3" followed by the "^" button (or its equivalent) and then enter "-1". Press "=" or "Enter" to get the result. The value should be approximately 0.3333. Next, clear the calculator and enter "4" followed by the "^" button (or its equivalent) and then enter "2". Press "=" or "Enter" to get the result. The value should be 16. Now, multiply 0.3333 by 16 using your calculator. The result should be approximately 5.333. Finally, raise the result to the power of 0.8. Clear the calculator, enter "5.333" followed by the "^" button (or its equivalent), and then enter "0.8". Press "=" or "Enter" to get the result. The value should be approximately 4.2162.

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