Evaluate: [tex]$4 y^0+x^1$[/tex] if [tex]$x=8$[/tex] and [tex]$y=7$[/tex]
Answer (1)
Substitute the given values: 4 ( 7 0 ) + ( 8 1 ) .
Simplify using exponent rules: 7 0 = 1 and 8 1 = 8 .
Perform the multiplication: 4 × 1 = 4 .
Add the results: 4 + 8 = 12 . The final answer is 12 .
Explanation
Understanding the Problem We are asked to evaluate the expression 4 y 0 + x 1 given that x = 8 and y = 7 . Let's break this down step by step.
Substitution First, we substitute the given values of x and y into the expression: 4 y 0 + x 1 = 4 ( 7 0 ) + ( 8 1 ) .
Simplification Next, we simplify the expression. Recall that any non-zero number raised to the power of 0 is 1. Therefore, 7 0 = 1 . Also, any number raised to the power of 1 is just the number itself, so 8 1 = 8 . Substituting these values, we get: 4 ( 1 ) + 8 .
Multiplication Now, we perform the multiplication: 4 × 1 = 4 . So the expression becomes: 4 + 8 .
Addition Finally, we perform the addition: 4 + 8 = 12 . Therefore, the value of the expression 4 y 0 + x 1 when x = 8 and y = 7 is 12.
Final Answer Thus, the final answer is 12.
Examples
Imagine you're calculating the total cost of items where some have a fixed cost and others vary. This problem is similar to finding the total cost when you have a fixed fee ( 4 y 0 ) and a variable cost ( x 1 ). For example, if you have a membership fee of $4 and you buy an item costing $8, the total cost is $4 + $8 = $12. Understanding how to evaluate such expressions helps in everyday calculations like budgeting and managing expenses.
