What is 7 to the power of 3 in expanded form?
The correct answer and explanation is:
Answer:
7 to the power of 3 in expanded form is:
7 × 7 × 7 = 343
Explanation (Approx. 300 Words):
In mathematics, when we talk about powers or exponents, we are referring to repeated multiplication of a number by itself. The expression “7 to the power of 3” is written as 7³. This means that the number 7 is used as a factor three times in a multiplication.
The number 7 is called the base, and the number 3 is the exponent or power. The exponent tells us how many times to multiply the base by itself. So, 7³ means:
7 × 7 × 7
Let’s solve it step by step:
- First, multiply the first two 7s:
7 × 7 = 49 - Then, multiply the result by the next 7:
49 × 7 = 343
So, 7³ = 343.
The expanded form, therefore, is simply writing the multiplication:
7 × 7 × 7
This method of writing powers in expanded form is especially useful for understanding what exponents mean, particularly for students learning about them for the first time. It helps to visualize and understand that exponents are not just shorthand, but a concept based on repeated multiplication.
Knowing how to expand powers is also important in algebra and more advanced math. For instance, when simplifying expressions or solving equations that involve exponents, understanding the expanded form can help avoid mistakes and deepen your understanding of how numbers behave.
In summary, 7 to the power of 3 in expanded form is:
7 × 7 × 7 = 343,
where 7 is the base, 3 is the exponent, and 343 is the final result of the repeated multiplication.