Raising a power to a power

Difficulty Starter · Set agiaor

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1
(4⁵)²=4 to the power of
2
(3³)²=3 to the power of
3
(4⁴)³=4 to the power of
4
(5⁴)³=5 to the power of
5
(2⁴)²=2 to the power of
6
(5⁴)³=5 to the power of
7
(3⁴)²=3 to the power of
8
(4⁵)²=4 to the power of
9
(2³)²=2 to the power of
10
(4⁴)³=4 to the power of
11
(2⁴)³=2 to the power of
12
(4³)²=4 to the power of
13
(3⁵)²=3 to the power of
14
(4⁴)²=4 to the power of
15
(5⁵)⁴=5 to the power of
16
(5⁴)³=5 to the power of
17
(3⁴)²=3 to the power of
18
(2⁵)³=2 to the power of
19
(5³)²=5 to the power of
20
(5³)²=5 to the power of

What is in this set

The numbers in this set run from 2 to 5.
A careful solution takes 1 written step on average.
The mistake this set invites most often, in 100% of the problems: the exponents were added; a power raised to a power multiplies them.
Answers are a whole number.

Drawing 240 problems from this page produced 24 different ones, 10% — 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.