Evaluate the following expression when x = 6 and y = 2:
x² + y³
2 + ×
The Correct Answer and Explanation is:
To evaluate the expression ( x^2 + y^3 ) when ( x = 6 ) and ( y = 2 ), follow these steps:
Step 1: Substitute the values of ( x ) and ( y ) into the expression.
The given expression is:
[
x^2 + y^3
]
Substitute ( x = 6 ) and ( y = 2 ):
[
6^2 + 2^3
]
Step 2: Calculate the powers of ( x ) and ( y ).
First, calculate ( 6^2 ):
[
6^2 = 6 \times 6 = 36
]
Next, calculate ( 2^3 ):
[
2^3 = 2 \times 2 \times 2 = 8
]
Step 3: Add the results.
Now, add the results of ( 6^2 ) and ( 2^3 ):
[
36 + 8 = 44
]
Final Answer:
The value of the expression ( x^2 + y^3 ) when ( x = 6 ) and ( y = 2 ) is 44.
Explanation:
The expression consists of two parts: ( x^2 ) and ( y^3 ). These parts involve exponentiation, where:
- ( x^2 ) means ( x ) multiplied by itself (the square of ( x )).
- ( y^3 ) means ( y ) multiplied by itself three times (the cube of ( y )).
By substituting the values of ( x ) and ( y ) into the expression, we compute ( 6^2 = 36 ) and ( 2^3 = 8 ). Then, we add the two results to obtain ( 36 + 8 = 44 ).
Understanding how to perform basic exponentiation (raising numbers to powers) and then applying those calculations is key in solving this type of problem.
This step-by-step approach ensures clarity and accuracy when evaluating similar expressions, and recognizing how to break down exponents into repeated multiplication is fundamental to solving such problems efficiently.