Powers Check Practice Questions
Powers check questions ask which expression is not equivalent to the original. The fastest method is to turn every expression into prime-power form, then compare the exponents rather than multiplying out large numbers.
The Rules Every Powers Check Question Uses
These questions are not about long multiplication. They are about rewriting expressions so the hidden mismatch becomes easy to see.
🔎 Rule 1: Convert to prime factors
Rewrite composite bases like 4, 8, 9, 36, and 64 using primes before comparing expressions.
Example: 93 × 8 = (32)3 × 23 = 23 × 36.
➕ Rule 2: Same base means add exponents
When powers with the same base are multiplied, add their exponents.
Example: 33 × 32 × 3 = 33+2+1 = 36.
🧱 Rule 3: Keep each prime base separate
Compare the exponent of 2, then the exponent of 3, then any 5s. One changed exponent makes the option different.
Example: 23 × 36 is not the same as 23 × 37.
⚠️ Rule 4: Do not compare by appearance
Different-looking expressions can still be equivalent after factorising. The only reliable comparison is the final prime-power form.
Example: 6 × 12 × 34 becomes 23 × 36.
3 Worked Powers Check Examples
One straightforward, one multi-step, and one classic mistake to avoid.
1. Spotting One Extra Power
Question: 93 × 8 is not equal to which option?
A. 23 × 37
B. 22 × 3 × 32 × 32 × 2 × 3
C. 6 × 12 × 34
D. 4 × 93 × 2
E. 36 × 23
Worked Method
Step 1: 93 = (32)3 = 36, and 8 = 23.
Step 2: The original expression is 23 × 36.
Step 3: Option A is 23 × 37, which has one extra factor of 3.
Answer: A. Tip: Compare exponents, not how complicated the option looks.
2. Combining Several Factors
Question: 3 × 8 × 9 × 9 is not equal to which option?
A. 34 × 3 × 22 × 2
B. 4 × 92 × 2 × 3
C. 6 × 12 × 33
D. 23 × 34
E. 34 × 3 × 23
Worked Method
Step 1: Convert the composite numbers: 8 = 23 and each 9 = 32.
Step 2: Combine the 3s: 3 × 32 × 32 = 31+2+2 = 35.
Step 3: The original is 23 × 35. Option D is 23 × 34, so it is missing one factor of 3.
Answer: D. Tip: A plain 3 counts as 31.
3. Similar-Looking Bases Can Hide a Missing Factor
Question: 22 × 9 × 42 is not equal to which option?
A. 43 × 9
B. 26 × 3
C. 32 × 24 × 22
D. 22 × 2 × 23 × 32
E. 22 × 23 × 2 × 3 × 3
Worked Method
Step 1: 9 = 32 and 42 = (22)2 = 24.
Step 2: Combine the 2s: 22 × 24 = 26, so the original is 26 × 32.
Step 3: Option B is 26 × 3. It has the correct power of 2 but only 31, not 32.
Answer: B. Tip: Do not stop after checking the power of 2. The power of 3 matters too.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Powers Check pack contains 90 questions across 3 printable test sets, with answer sheets covering exponent rules, powers and indices, prime factorisation, equivalent expressions, and spotting the one non-matching option.
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