Algebra: Index Laws and Zero Index

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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?

$\left(\frac{a}{b}\right)^m = \frac{a^m}{b^m}$ 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?

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

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

$1$ Signup and view all the answers

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

$1$ Signup and view all the answers

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

$1$ Signup and view all the answers

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

$25$ Signup and view all the answers

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

$1$ Signup and view all the answers

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?

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 $a^m \cdot b^m = (ab)^m$ 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 $a^{-m} = \frac{1}{a^m}$ 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?

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

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

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

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

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

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