In the context of mathematical expressions, which of the following statements ab

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Question: In the context of mathematical expressions, which of the following statements about exponents is true?

Options:

Correct Answer: The product of two numbers with the same base is the sum of their exponents.

Solution:

The product of two numbers with the same base is indeed the sum of their exponents, as per the laws of exponents.

In the context of mathematical expressions, which of the following statements about exponents is true?

In the context of mathematical expressions, which of the following statements about exponents is true?

Step 1: Understand what an exponent is. An exponent shows how many times a number (the base) is multiplied by itself.
Step 2: Identify the base in the expression. For example, in 2^3, the base is 2.
Step 3: Look at the exponents. In the expression 2^3 * 2^4, the exponents are 3 and 4.
Step 4: Apply the law of exponents for multiplication. When you multiply two numbers with the same base, you add their exponents.
Step 5: Calculate the sum of the exponents. In this case, 3 + 4 = 7.
Step 6: Write the result using the base and the new exponent. So, 2^3 * 2^4 = 2^(3+4) = 2^7.

Laws of Exponents – The rules governing the operations involving exponents, such as the product of powers rule which states that when multiplying two numbers with the same base, you add their exponents.