Evaluating the Expression: 20 × 2 × 5¹ - 30 × 3⁴ + 14 × 58
When dealing with mathematical expressions, it's essential to follow the order of operations (PEMDAS) to ensure accurate results. In this article, we'll break down the given expression, step by step, to evaluate its value.
The Expression: 20 × 2 × 5¹ - 30 × 3⁴ + 14 × 58
Let's start by identifying the different components of the expression:
- Exponents: 5¹ and 3⁴
- Multiplications: 20 × 2, 30 × 3⁴, and 14 × 58
- Subtraction: -
Step 1: Evaluate the Exponents
First, let's evaluate the exponents:
- 5¹ = 5 (since any number raised to the power of 1 is itself)
Next, we have:
- 3⁴ = 3 × 3 × 3 × 3 = 81
Step 2: Evaluate the Multiplications
Now, let's evaluate the multiplications:
- 20 × 2 = 40
- 30 × 81 = 2430
- 14 × 58 = 812
Step 3: Evaluate the Expression
Now that we have evaluated the exponents and multiplications, we can put it all together:
- 40 × 5 = 200
- 200 - 2430 = -2230
- -2230 + 812 = -1418
Final Answer:
The final value of the expression 20 × 2 × 5¹ - 30 × 3⁴ + 14 × 58 is -1418.
