Final answer:
The expression 8²+9(12/3x²)-7 simplifies to 57 + 36x² after performing the order of operations, simplifying within the parentheses, and combining like terms.
Step-by-step explanation:
The question involves simplifying a mathematical expression, which is a common task in algebra. Let's go through the given expression step by step:
Simplify the expression 8²+9(12/3x²)-7. First, perform the operations inside the parentheses: 12 divided by 3 equals 4. Therefore, the expression inside the parentheses simplifies to 9*4x², or 36x².
Next, we'll incorporate the simplified value back into the original expression:
8² + 36x² - 7. The square of 8 is 64, so the expression becomes 64 + 36x² - 7.
Finally, eliminate terms by combining like terms, if possible. As there are no like terms to combine with 36x², we'll only combine the constant terms, 64 and -7, which gives us 57.
The simplified expression is thus 57 + 36x².
To check the answer for reasonability, ensure that all operations were performed correctly and appropriate properties of exponents and arithmetic were applied.