Dividing powers of one base

Difficulty Standard · Set 18z5i8

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1
6⁷÷6³=6 to the power of
2
6³÷6²=6 to the power of
3
8³÷8²=8 to the power of
4
2⁵÷2³=2 to the power of
5
7⁸÷7⁵=7 to the power of
6
8⁸÷8²=8 to the power of
7
6⁷÷6⁵=6 to the power of
8
3⁸÷3³=3 to the power of
9
6⁵÷6⁴=6 to the power of
10
5⁹÷5⁷=5 to the power of
11
2⁵÷2⁴=2 to the power of
12
9⁶÷9²=9 to the power of
13
8³÷8²=8 to the power of
14
4⁴÷4²=4 to the power of
15
8⁹÷8⁷=8 to the power of
16
3⁵÷3³=3 to the power of
17
9⁷÷9³=9 to the power of
18
5⁶÷5⁵=5 to the power of
19
3⁴÷3³=3 to the power of
20
9⁸÷9⁵=9 to the power of

What is in this set

The numbers in this set run from 2 to 9.
A careful solution takes 1 written step on average.
The mistake this set invites most often, in 16% of the problems: the exponents were divided; dividing powers of the same base takes one away from the other.
Answers are a whole number.

Drawing 240 problems from this page produced 138 different ones, 57% — so a sheet of 20 will come back to a problem you have seen — there are only so many sensible ones of this kind.

The same skill, harder or easier

We would put this in front of a grade 8 class. That is our judgement, not a standard, and it is printed here so you can disagree with it. Everything else we put in that year.