# Rational and Exponents

> TSI Math Test Study Guide · Hightower High School P-TECH (2023)
>
> Source: [complete Markdown guide](../TSI-Math-Test-Study-Guide.md) · [original PDF](../1062198634-Hightower-TSI-Test-Study-Guide-v2-MATH.pdf)


#### 1. $\left(\frac{7}{x}\right)^2$ = ?

**A.** $\frac{14}{x^2}$

**B.** $\frac{49}{x^2}$

**C.** $\frac{7^2}{x}$

**D.** $\frac{x^2}{49}$


#### 2. $\left(\frac{5a}{b}\right)^2 = ?$

**A.** $\frac{5a^2}{b^2}$

**B.** $\frac{25a}{b^2}$

**C.** $\frac{25a^2}{b^2}$

**D.** $\frac{10a^2}{b}$



#### 3. $\left(\frac{2r}{3s}\right)^2$ = ?

**A.** $\frac{2r^2}{(3s^2)}$

**B.** $\frac{2r}{(3s^2)}$

**C.** $\frac{4r^2}{(9s^2)}$

**D.** $\frac{9s^2}{(4r^2)}$


#### 4. $\left(\frac{12}{b}\right)^2$ = ?

**A.** $\frac{24}{b^2}$

**B.** $\frac{12}{b}$

**C.** $\frac{144}{b}$

**D.** $\frac{144}{b^2}$


#### 5. $\frac{m^{10}}{m^2}$ = ?

**A.** m⁵

**B.** m⁸

**C.** $\frac{1}{m⁵}$

**D.** $\frac{1}{m⁸}$


#### 6. If $h(x) = 10^x$, then for what value of x does h(x) = 1,000,000?

**A.** 2

**B.** 4

**C.** 6

**D.** 8


#### 7. For what value of $x$ is the function $g(x) = \frac{x}{1-x}$ not defined?

**A.** 0

**B.** 1

**C.** 2

**D.** 3


#### 8. For what value of a would (ax − b) / a not be defined?

**A.** 0

**B.** 1

**C.** 2

**D.** 3


#### 9. If a ≠ 0, a ≠ 1, and (ax − b) / (a − 1) = b, what is the value of x?

**A.** $b$

**B.** 1

**C.** $a$

**D.** $\frac{b}{a}$


#### 10. If a ≠ 0, a ≠ 3, and (ax − 3b) / (a − 3) = b, what is the value of x?

**A.** $b$

**B.** 1

**C.** $a$

**D.** 3