High school math test questions on negative exponents

📚 Quick Study Guide

• 🔢 A negative exponent means you take the reciprocal of the base raised to the positive of that exponent. For example, $x^{-n} = \frac{1}{x^n}$.
• 💡 Any non-zero number raised to the power of 0 is 1. That is, $x^0 = 1$ (if $x \neq 0$).
• ➗ When dividing exponential terms with the same base, you subtract the exponents: $\frac{x^a}{x^b} = x^{a-b}$. This rule works even if $a-b$ is negative.
• 🧪 When you have a power raised to another power, you multiply the exponents: $(x^a)^b = x^{ab}$. This also applies to negative exponents.
• 📝 A negative exponent does *not* make the number negative. It indicates a reciprocal.

Practice Quiz

1. What is the value of $2^{-3}$?
   1. $\frac{1}{8}$
   2. $-8$
   3. $8$
   4. $-\frac{1}{8}$
2. Simplify $x^{-5}$:
   1. $\frac{1}{x^5}$
   2. $-x^5$
   3. $x^5$
   4. $\frac{1}{5x}$
3. What is the value of $(-3)^{-2}$?
   1. $\frac{1}{9}$
   2. $-9$
   3. $9$
   4. $-\frac{1}{9}$
4. Simplify $\frac{y^2}{y^5}$:
   1. $y^{-3}$
   2. $y^3$
   3. $\frac{1}{y^3}$
   4. $\frac{1}{y^{-3}}$
5. What is the value of $5^0 + 5^{-1}$?
   1. $1.2$
   2. $0$
   3. $6$
   4. $1$
6. Simplify $(a^{-2})^{-3}$:
   1. $a^{-5}$
   2. $a^{-6}$
   3. $a^6$
   4. $\frac{1}{a^5}$
7. What is $4^{-1} + 2^{-2}$?
   1. $0$
   2. $\frac{1}{2}$
   3. $\frac{1}{8}$
   4. $4$