A $205$-ft long escalator at the CNN World Headquarters in Atlanta, Georgia, is the world's longest freestanding escalator. In a rush, Dominik walks up the escalator at a rate of $100 \mathrm{ft} / \mathrm{min}$ while the escalator is moving up at a rate of $105 \mathrm{ft} / \mathrm{min}$. How long will it take him to reach the top of the escalator?

Multiply and simplify. Leave the answer in exponential notation.

$$m^0 \cdot m^8$$

Find whether the two equations in the pair are equivalent. $12-x=3$ and $2 x=20$

Use a commutative law to write an expression equivalent to $3+x$.

Compute using the rules for the order of operations. If an expression is undefined, state this.

$$\dfrac{(2-3)^3-5|2-4|}{7-2 \cdot 5^2}$$

Simplify. Suppose that all variables represent nonzero integers.

$$\dfrac{3^{q+3}-3^2\left(3^q\right)}{3\left(3^{q+4}\right)}$$

Simplify. Suppose that all variables represent nonzero integers.

$$\dfrac{4 x^{2 a+3} y^{2 b-1}}{2 x^{a+1} y^{b+1}}$$

Compute using the rules for the order of operations. If an expression is undefined, state this.

$$\dfrac{4^3-(7-4)^2}{3^2-7}$$

Compute using the rules for the order of operations. If an expression is undefined, state this.

$$\dfrac{3^4-(5-3)^4}{8-2^3}$$

Simplify. Suppose that all variables represent nonzero integers.

$$\dfrac{-28 x^{b+5} y^{4+c}}{7 x^{b-5} y^{c-4}}$$

Simplify. Suppose that all variables represent nonzero integers.

$$\left(3^{a+2}\right)^a$$

Compute using the rules for the order of operations. If an expression is undefined, state this.

$$\dfrac{7 \cdot 3-5^2}{9+4 \cdot 2}$$

Compute using the rules for the order of operations. If an expression is undefined, state this.

$$\dfrac{5 \cdot 2-4^2}{27-2^4}$$

Simplify. Suppose that all variables represent nonzero integers.

$$\left\{\left[\left(8^{-a}\right)^{-2}\right]^b\right\}^{-c} \cdot\left[\left(8^0\right)^a\right]^c$$