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Questions and Answers
What is the value of $x^0$, where $x$ is a non-zero real number?
What is the value of $x^0$, where $x$ is a non-zero real number?
- $0$
- Undefined
- $x$
- $1$ (correct)
Which expression is equivalent to $x^3 \cdot x^{-2}$?
Which expression is equivalent to $x^3 \cdot x^{-2}$?
- $x^5$
- $\frac{1}{x}$
- $x$ (correct)
- $\frac{1}{x^5}$
If $a^2 = 9$ and $b^3 = 27$, what is the value of $(ab)^5$?
If $a^2 = 9$ and $b^3 = 27$, what is the value of $(ab)^5$?
- $243$
- $6561$
- $177147$
- $59049$ (correct)
Which of the following is the correct algebraic form of the index law $x^m \cdot x^n = x^{m+n}$?
Which of the following is the correct algebraic form of the index law $x^m \cdot x^n = x^{m+n}$?
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If $x^4 = 16$ and $y^2 = 9$, what is the value of $\left(\frac{x^2}{y}\right)^3$?
If $x^4 = 16$ and $y^2 = 9$, what is the value of $\left(\frac{x^2}{y}\right)^3$?
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Study Notes
Index Laws
- Index laws can be extended and applied to variables using positive-integer indices and the zero index.
- The index laws for numerical bases with positive-integer indices can be used to develop the index laws in algebraic form.
Index Laws in Algebraic Form
- The index laws can be expressed in algebraic form using variables and positive-integer indices.
x^0 = 1
- x^0 = 1 can be established algebraically using the index laws.
- This is a fundamental property of indices and is used to simplify algebraic expressions.
Simplifying Algebraic Expressions
- Algebraic expressions that involve the zero index can be simplified using the index laws.
- Simplifying expressions involving the zero index is important in algebraic manipulations and equations.
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