melissadouglas1988
melissadouglas1988 5d ago โ€ข 0 views

High school math test questions on negative exponents

Hey there! ๐Ÿ‘‹ Negative exponents can seem tricky, but they're actually super useful in math and science. Let's break them down and then test your knowledge with a quick quiz! ๐Ÿค“
๐Ÿงฎ Mathematics

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๐Ÿ“š Quick Study Guide

  • ๐Ÿ”ข A negative exponent means you take the reciprocal of the base raised to the positive of that exponent. For example, $x^{-n} = \frac{1}{x^n}$.
  • ๐Ÿ’ก Any non-zero number raised to the power of 0 is 1. That is, $x^0 = 1$ (if $x \neq 0$).
  • โž— 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.
  • ๐Ÿงช When you have a power raised to another power, you multiply the exponents: $(x^a)^b = x^{ab}$. This also applies to negative exponents.
  • ๐Ÿ“ 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. $4$
Click to see Answers
  1. A
  2. A
  3. A
  4. C
  5. A
  6. C
  7. B

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