X^m

Definition

The term $x^m$ represents the mathematical expression where $x$ is a variable and $m$ is the exponent. It denotes the operation of raising $x$ to the power of $m$, which results in multiplying $x$ by itself $m$ times.

5 Must Know Facts For Your Next Test

1. The exponent $m$ in $x^m$ represents the number of times the variable $x$ is multiplied by itself.
2. When $m$ is a positive integer, $x^m$ can be interpreted as the product of $m$ factors of $x$.
3. If $m$ is a negative integer, $x^m$ represents the reciprocal of $x$ raised to the power of $|m|$.
4. The value of $x^m$ is dependent on both the value of $x$ and the value of the exponent $m$.
5. Exponents with the same base can be multiplied by adding the exponents, and exponents with the same base can be divided by subtracting the exponents.

Review Questions

• Explain the meaning and interpretation of the term $x^m$ in the context of exponents.
  • The term $x^m$ represents the operation of raising the variable $x$ to the power of $m$. This means that $x$ is multiplied by itself $m$ times. For example, $x^3$ would be interpreted as $x \times x \times x$, which is the product of three factors of $x$. The exponent $m$ determines how many times the base $x$ is used as a factor in the expression.
• Describe the properties of exponents that can be applied to the term $x^m$.
  • The properties of exponents that can be applied to $x^m$ include: 1) $x^m \times x^n = x^{m+n}$: Exponents with the same base can be multiplied by adding the exponents. 2) $x^m \div x^n = x^{m-n}$: Exponents with the same base can be divided by subtracting the exponents. 3) $(x^m)^n = x^{m \times n}$: Exponents can be raised to a power by multiplying the exponents.
• Analyze the impact of the exponent $m$ on the value of $x^m$ and explain how this relationship can be used to simplify expressions.
  • The value of $x^m$ is directly dependent on the value of the exponent $m$. When $m$ is a positive integer, $x^m$ represents the repeated multiplication of $x$ by itself $m$ times, resulting in a larger value. Conversely, when $m$ is a negative integer, $x^m$ represents the reciprocal of $x$ raised to the power of $|m|$, resulting in a smaller value. This relationship can be used to simplify expressions involving exponents, such as by applying the properties of exponents to combine or cancel out terms with the same base.

Related terms

Exponent:

The exponent is the small number placed to the upper right of a base number, which indicates how many times the base is used as a factor.

Power:

Power is the result of raising a number or variable to an exponent, which represents repeated multiplication of the base.

Base:

The base is the number or variable that is raised to a power, which is then multiplied by itself the number of times indicated by the exponent.