3 mistakes learners make with powers and indices, each one named and explained.
A power counts how many copies of the base are multiplied, so multiplying powers of the same base adds those counts.
2 to the 3 times 2 squared is answered as 2 to the 6.
The question says multiply, so the powers get multiplied along with everything else.
Question. 2 to the 3, times 2 squared
A common answer. 2 to the 6, which is 64
The answer. 2 to the 5, which is 32
Why. There are three 2s and then two more 2s, so five 2s are multiplied in total.
Multiplying powers adds the indices. Raising a power to a power multiplies them.
2 to the power 3 is worked out as 2 times 3, so 2 to the power -3 comes out as -6.
The index is written like a small number next to the base, and multiplying is what numbers written next to each other usually means.
Question. 2 to the power 3
A common answer. 6, which is 2 times 3
The answer. 8
Why. The index counts the copies, so it means 2 times 2 times 2.
The index is a count of copies, never a thing you multiply by.
(-3) squared is answered as -9.
The minus sign gets carried through out of habit, because it usually does survive.
Question. (-3) squared
A common answer. -9
The answer. 9
Why. It means -3 x -3, and two negatives multiplied give a positive.
The brackets decide what is being squared, so read them first.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.