Raising a power to a power

Difficulty Standard · Set 9fdotx

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1
(2⁵)³=2 to the power of
2
(8⁸)²=8 to the power of
3
(5⁵)²=5 to the power of
4
(8⁸)³=8 to the power of
5
(7⁴)³=7 to the power of
6
(5³)²=5 to the power of
7
(8⁸)⁶=8 to the power of
8
(5⁵)³=5 to the power of
9
(9⁶)⁴=9 to the power of
10
(4³)²=4 to the power of
11
(4⁹)³=4 to the power of
12
(2⁹)³=2 to the power of
13
(5⁴)³=5 to the power of
14
(7⁶)⁴=7 to the power of
15
(6⁷)⁶=6 to the power of
16
(7⁵)²=7 to the power of
17
(3⁸)⁵=3 to the power of
18
(4⁴)²=4 to the power of
19
(2⁸)⁶=2 to the power of
20
(6⁶)⁵=6 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 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 137 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.