EDGE Math 8

1.	Which of the following equations is false?

{(3 \cdot 2)}^{2} = 2^{2} \cdot 3^{2}

3 \cdot 2^{2} = 2 \cdot 6

3 \cdot 2^{2} = 6^{2}

none of the choices

Answer: $3 \cdot 2^{2} = 6^{2}$

2.	Consider the exponential expression $a^{- n},$ where $n$ is a positive integer. Which of the following statements is true?

The variable

a

cannot be equal to 0.

The value of

a^{- n}

can be equal to 0.

The value of

a^{- n}

is always less than –1.

none of the choices

Answer: The variable $a$ cannot be equal to 0.

3.	Which of the following is equal to ${(a + b)}^{3} ?$ (Hint: You may verify the answer by assuming certain values for $a$ and $b .)$

a^{3} + b^{3}

a^{3} + 3 a^{2} b^{2} + b^{3}

a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

none of the choices

Answer: $a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$

4.	Let $m$ be a positive integer, and $a$ and $b$ be nonzero real numbers. Which of the following is equal to ${(\frac{a}{b})}^{- m} ?$

{(\frac{b}{a})}^{m}

- \frac{a^{m}}{b^{m}}

\frac{1}{a^{m} b^{m}}

none of the choices

Answer: ${(\frac{b}{a})}^{m}$