Simplifying and solving equations with exponents
- Firstly, it's important to remember that when solving equations with exponents like this, you'll want to simplify the bracketed expressions first before raising them to a power. So in this case, you would simplify the expressions inside the brackets to get (6)^2 and (6x)^2.
- Next, you can apply the power of a power rule, which states that when raising a power to another power, you simply multiply the exponents together. So in this case, (6)^2 becomes 6^(2*2) and (6x)^2 becomes (6x)^(2*2).
- After simplifying the expressions, you should end up with (36)^2 and (36x)^2.
- Finally, you can combine the terms by multiplying the coefficients together and keeping the bases the same. So for the first term, you would have (36)^2 = 36*36 = 1296 and for the second term, you would have (36x)^2 = 36^2 * x^2 = 1296x^2.
- Don't forget the order of operations- multiplication and division are done first, followed by addition and subtraction. So make sure to distribute any coefficients before multiplying, as shown in step 4.
- If you're ever struggling with exponent rules, just remember the mnemonic PEMDAS- Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. This can help you keep track of which operations to do first.
- Another helpful tip is to break down the problem one step at a time and write out each step clearly. This will help you avoid making mistakes or getting lost in the calculations.
- Lastly, always double check your answer by plugging the value of x back into the original equation to make sure it holds true. This can save you from getting the wrong answer due to a small mistake.
