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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?
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?
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?
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?
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?
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?
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?
What is the value of $x^5 \cdot x^0$?
What is the value of $x^5 \cdot x^0$?
Simplify $a^6 \div a^6$.
Simplify $a^6 \div a^6$.
What is the value of $m^3 \cdot m^{-3}$?
What is the value of $m^3 \cdot m^{-3}$?
Evaluate $5^2 \cdot 5^0$.
Evaluate $5^2 \cdot 5^0$.
Simplify $c^{-3} \cdot c^{-3}$.
Simplify $c^{-3} \cdot c^{-3}$.
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