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Powers & roots

1. pow-01 Present from here

   Work out $5^2$

   A Option A: $10$

   B Option B: $32$

   C Option C: $25$

   D Option D: $7$
   Answer and misconceptions

   A Option A: $10$ ✗

   Multiplies the base by the powerHas done 5 × 2 instead of 5 × 5.

   B Option B: $32$ ✗

   Swaps the base and the powerHas worked out 2⁵ = 32.

   C Option C: $25$ ✓ Correct

   D Option D: $7$ ✗

   Adds the base and the powerHas done 5 + 2.
2. pow-02 Present from here

   Work out $\sqrt{64}$

   A Option A: $8$

   B Option B: $32$

   C Option C: $4$

   D Option D: $4096$
   Answer and misconceptions

   A Option A: $8$ ✓ Correct

   B Option B: $32$ ✗

   Halves the number for a square rootThinks square root means divide by 2.

   C Option C: $4$ ✗

   Finds the cube root instead4 × 4 × 4 = 64, so has confused √ with ∛.

   D Option D: $4096$ ✗

   Squares the number instead of rooting itHas done 64 × 64.
3. pow-03 Present from here

   Work out $(-4)^2$

   A Option A: $-16$

   B Option B: $-8$

   C Option C: $-2$

   D Option D: $16$
   Answer and misconceptions

   A Option A: $-16$ ✗

   Thinks squaring a negative gives a negativeNegative × negative is positive: (−4) × (−4) = 16.

   B Option B: $-8$ ✗

   Multiplies by 2, keeping the signHas done −4 × 2.

   C Option C: $-2$ ✗

   Confuses squaring with square rootingTakes the square root of 4 and keeps the minus sign, giving −2.

   D Option D: $16$ ✓ Correct
4. pow-04 Present from here

   Simplify $2^3 \times 2^4$

   A Option A: $2^{12}$

   B Option B: $2^{7}$

   C Option C: $4^{7}$

   D Option D: $2^{1}$
   Answer and misconceptions

   A Option A: $2^{12}$ ✗

   Multiplies the indicesHas done 3 × 4; when multiplying powers of the same base, add the indices.

   B Option B: $2^{7}$ ✓ Correct

   C Option C: $4^{7}$ ✗

   Multiplies the bases as well as adding indicesHas done 2 × 2 = 4 for the base; the base stays as 2.

   D Option D: $2^{1}$ ✗

   Subtracts the indicesHas used the division law (4 − 3) for a multiplication.
5. pow-05 Present from here

   Work out $3^{-2}$

   A Option A: $-9$

   B Option B: $-6$

   C Option C: $\frac{1}{9}$

   D Option D: $9$
   Answer and misconceptions

   A Option A: $-9$ ✗

   Thinks a negative index makes the answer negativeA negative index means a reciprocal: 1/3² = 1/9.

   B Option B: $-6$ ✗

   Multiplies the base by the indexHas done 3 × −2.

   C Option C: $\frac{1}{9}$ ✓ Correct

   D Option D: $9$ ✗

   Ignores the negative sign in the indexHas worked out 3² instead of 3⁻².