What does x raised to the power of 4 mean?

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X raised to the power of 4, often written as x4, is a mathematical expression that indicates the value of x multiplied by itself a total of four times. In simpler terms, it represents the product:

x × x × x × x

This expression implies that whatever value you assign to x, you will multiply that value by itself three more times. For instance:

  • If x = 2, then x4 = 24 = 2 × 2 × 2 × 2 = 16.
  • If x = -3, then x4 = (-3)4 = -3 × -3 × -3 × -3 = 81.

Notice that when x is a negative number, raising it to the fourth power results in a positive number because multiplying two negative numbers yields a positive result, as seen in the second example.

This concept is not limited to integers; it can also apply to fractions, decimals, and variables. For example, if x = rac{1}{2}, then:

x4 = rac{1}{2}4 = rac{1}{2} × rac{1}{2} × rac{1}{2} × rac{1}{2} = rac{1}{16}

Raising a number to the fourth power is commonly used in various fields, including physics and engineering, to express certain quantities such as volume (for cubic dimensions), but in this context, it’s important to note it fundamentally describes exponential growth and algebraic manipulation.

In conclusion, x4 signifies a number multiplied by itself four times, and its behavior can vary based on the value of x, showcasing both positive and interesting mathematical properties!

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