**Common mistakes that students make ..**

Multiplying base and exponent

Incorrect: 2

^{3}≠ 2 x 3 Correct: 2

Exponents "distribute"

Incorrect: (2 + 4)

Correct: (2 + 4)

Anything to the power of "zero" is? ...

Incorrect: 7

Correct: 7

Proof: 7

Scientific Notation! A negative on an exponent and a negative on a number ... uhh? Are they the same?

^{3 }= 2 x 2 x 2 = 8Exponents "distribute"

Incorrect: (2 + 4)

^{3}≠ 2^{3}+ 4^{3}Correct: (2 + 4)

^{3}= 6^{3}= 6 x 6 x 6 =216Anything to the power of "zero" is? ...

Incorrect: 7

^{0}≠ 0Correct: 7

^{0}= 1Proof: 7

^{0}= 7^{(m-m) }= 7^{m }÷ 7^{m}= 1 (anything divided by itself is just "1")Scientific Notation! A negative on an exponent and a negative on a number ... uhh? Are they the same?

Correct: 0.00036 = 3.6 × 10

^{-4 }^{ -0.00036 = -3.6 × 10-4 }

^{ 36,000 = 3.6 × 104}

^{ -36,000 = -3.6 × 104}

A negative on an exponent and a negative on a number are equal

Incorrect: -4

^{2}≠ 16 Correct: -4

^{2}= -16 Correct: -4

^{2}= -(4)^{2 }= -16 Correct: (-4)

^{2}= 16**How to fix this?**

(3 x 2)² = 3² x 2² then (3 + 2)² = 3² + 2², or the exponent rules when multiplying numbers with exponents is applicable to all operations.

Perhaps further examples can be used to illustrate this point:

i.e. (pq)³ = (pq) x (pq) x (pq) = (p x p x p) x (q x q x q) = p³ x q³

(p + q)³ = (p + q) x (p + q) x (p + q) = use of distributive property to solve.

i.e. (3 x 4)³ = (3 x 4) x (3 x 4) x (3 x 4) = (3 x 3 x 3) x (4 x 4 x 4) = 3³ x 4³, which is same as 12³ but

i.e. (3 + 4)³ = (3 + 4) x (3 + 4) x (3 +4) = 7³, which is not the same as 3³ + 4³