Algebra: Index Laws and Zero Index
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Questions and Answers

Which of the following expressions represents the index law for raising a variable to the power of zero?

  • $x^0 = 0$
  • $x^0 = \frac{1}{x}$
  • $x^0 = x$
  • $x^0 = 1$ (correct)
  • If $a^m \cdot a^n = a^{m+n}$ is the index law for multiplying variables with the same base, what is the index law for dividing variables with the same base?

  • $\frac{a^m}{a^n} = a^{m+n}$
  • $\frac{a^m}{a^n} = \frac{m}{n}$
  • $\frac{a^m}{a^n} = a^{mn}$
  • $\frac{a^m}{a^n} = a^{m-n}$ (correct)
  • If $a^m \cdot b^m = (ab)^m$ is the index law for multiplying variables with different bases, what is the index law for raising a product of variables to a power?

  • $(ab)^m = a^m \cdot b^m$ (correct)
  • $(ab)^m = a^{m+1} \cdot b^{m-1}$
  • $(ab)^m = a^{mb} \cdot b^{ma}$
  • $(ab)^m = a^m \cdot b^m \cdot m$
  • If $a^{-m} = \frac{1}{a^m}$ is the index law for negative exponents, what is the index law for raising a quotient of variables to a power?

    <p>$\left(\frac{a}{b}\right)^m = \frac{a^m}{b^m}$</p> Signup and view all the answers

    If $(x^2)^3 = x^6$ is an example of the index law for raising a power to a power, what is the index law for raising a variable to the power of a quotient?

    <p>$x^{\frac{m}{n}} = \left(x^m\right)^\frac{1}{n}$</p> Signup and view all the answers

    What is the value of $x^5 \cdot x^0$?

    <p>$1$</p> Signup and view all the answers

    Simplify $a^6 \div a^6$.

    <p>$1$</p> Signup and view all the answers

    What is the value of $m^3 \cdot m^{-3}$?

    <p>$1$</p> Signup and view all the answers

    Evaluate $5^2 \cdot 5^0$.

    <p>$25$</p> Signup and view all the answers

    Simplify $c^{-3} \cdot c^{-3}$.

    <p>$1$</p> Signup and view all the answers

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