Algebra LS-2 Quiz v4

Apply the "product rule" to the following expression as a (single) base raised to a (single) power.

q^{-9}q^{3n}

Apply the "quotient rule" to the following expression to generate an equivalent expression.

\frac{x^{6}y^{-2}}{x^{2}y^{3}}

HINT: If you're having trouble, split the problem into two, easier problems by rewriting the expression as a product \frac{h^{m}x^{-3}}{h^{n}x}=\frac{h^{m}}{h^{n}}\cdot \frac{x^{-3}}{x}

Which of the following is equivalent to \big(\frac{1}{2x}\big)^{-3}? Select all that apply.

Evaluate the expression if t=7.

\big(3^{2}x^{t-7}\big)^{2}

Use the laws of exponents to generate a simplified expression.

\frac{(xyz)^{2}}{x^{5}z}

Terrance tries to re-write the expression \big(m^{-3}\cdot m^{2}\big)^{-1}. Here is his work.

Step 0: \big(m^{-3}\cdot m^{2}\big)^{-1}

Step 1: =\big(m^{(-3+2)}\big)^{-1}

Step 2: =\big(m^{-1}\big)^{-1}

Step 3: =-\big(m^{-1}\big)^{1}

Step 4: =-m^{-1}

Step 5: =-\frac{1}{m}

Did Terrance make a mistake? Select all that apply.

Emmy is working through the same problem using a different strategy. Here is her work.

Step 0: \big(m^{-3}\cdot m^{2}\big)^{-1}

Step 1: =\frac{1}{m^{-3}\cdot m^{2}}

Step 2: =\frac{1}{m^{(-3+2)}}

Step 3: =\frac{1}{m^{-1}}

Step 4: =\frac{m^{0}}{m^{-1}}

Step 5: =m^{(0--1)}

Step 6: =m^{1}

Which statement best describes Emmy's accuracy?

Use the laws of exponents to simplify the expression.

Use the laws of exponents to simplify the expression.