is there any trick I can use to solve the question below without expanding:
2^3 + 2^4
2^3 + 2^4
= 8 + 16
= 24
Don't know how much simpler we can make it.
How were you going to "expand" it?
Like there are rules for multipling eponents with the same base, I was wondering if there were rules for addition. If I were to get some complicated like:
3^-2/3 + 3^5/8
... it would take a longer time to solve.
no
If the bases are different, you cannot add or subtract them
e.g. x^3 + y^2 stays that way
If the bases are the same in addition, you can usually factor.
e.g. x^5 + x^2 = x^2(x^3 + 1)
Thank you :)
Yes, there is a trick you can use to solve the question without expanding. It involves using the concept of exponentiation and recognizing a pattern.
The given question is 2^3 + 2^4. Let's analyze the powers of 2 involved:
2^3 = 2 × 2 × 2 = 8
2^4 = 2 × 2 × 2 × 2 = 16
To find the sum of 2^3 + 2^4 without expanding, we can notice that the only difference between the two terms is an additional factor of 2. This means that 2^3 + 2^4 = 8 + 2 × 8.
Using this pattern, we can simplify the expression even further:
2^3 + 2^4 = 8 + 2 × 8
= 8 + 16
= 24
Hence, the answer to 2^3 + 2^4 without expanding is 24.