Practice Repeated Operations in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Applying the same operation multiple times in succession, where the repetition is often compressed into a higher-level operation: repeated addition becomes multiplication (nan \cdot a), and repeated multiplication becomes exponentiation (ana^n).

Adding 5 three times: 5+5+5=3×55+5+5 = 3 \times 5. Multiplying 2 four times: 2×2×2×2=242 \times 2 \times 2 \times 2 = 2^4.

Showing a random 20 of 50 problems.

Example 1

medium
A staircase pattern uses 1,3,5,7,1,3,5,7,\dots blocks per step. How many blocks in step 6?

Example 2

medium
A bacteria doubles every hour starting at 4. How many after 3 hours?

Example 3

hard
How many times must you multiply 2 by itself to reach 128?

Example 4

medium
Write 1010106 times\underbrace{10\cdot 10\cdots 10}_{6 \text{ times}} as a power and compute.

Example 5

easy
Write 4+4+4+4+44+4+4+4+4 as a multiplication.

Example 6

easy
How many times is 8 added in 6×86\times 8?

Example 7

hard
Aiden saves \$6 each week for 1 year (52 weeks). How much does he save? Express both as repeated addition and as a product.

Example 8

hard
If n×9=72n\times 9 = 72, find nn using the repeated-addition view.

Example 9

easy
Start at 50 and subtract 7 repeatedly. Write the first 4 results.

Example 10

easy
Start at 12 and subtract 3 repeatedly. Write the first 5 results.

Example 11

medium
Rewrite a+a+a+a+a+a+aa+a+a+a+a+a+a using multiplication.

Example 12

easy
Write 10+10+1010+10+10 as a multiplication and find the value.

Example 13

challenge
A snail climbs 3 ft each day and slips back 1 ft each night, then repeats. After 10 full day-night cycles, how far up is it?

Example 14

hard
A piece of paper is folded in half 8 times. How many layers are there after the last fold?

Example 15

easy
What is 333^3?

Example 16

easy
What is 525^2?

Example 17

medium
A jar gets 5 marbles added each day. After 12 days, how many marbles have been added?

Example 18

medium
Write 2+2++220 times\underbrace{2+2+\cdots+2}_{20 \text{ times}} as a product.

Example 19

medium
A pattern adds 3 each step starting at 5: 5,8,11,5,8,11,\dots. Write the value of step nn.

Example 20

easy
Rewrite 5×5×5×55\times 5\times 5\times 5 as a power.