Which is equal to $7 \times 7 \times 7 \times 7 \times 7 \times 7 ?$
A. $49 \times 49$
B. $7^6$
C. $6^7$
D. $6 \times 7$
Answer (1)
Rewrite the given expression 7 × 7 × 7 × 7 × 7 × 7 using exponents as 7 6 .
Compare 7 6 with the given options.
Eliminate options that are not equal to 7 6 .
The expression 7 × 7 × 7 × 7 × 7 × 7 is equal to 7 6 .
Explanation
Understanding the Problem We are given the expression 7 × 7 × 7 × 7 × 7 × 7 . We need to find an equivalent expression from the given options: 49 × 49 , 7 6 , 6 7 , 6 × 7 .
Rewriting with Exponents Let's rewrite the given expression using exponents. The expression 7 × 7 × 7 × 7 × 7 × 7 means 7 multiplied by itself 6 times, which can be written as 7 6 .
Comparing with Options Now, let's compare 7 6 with the given options:
49 × 49 = ( 7 × 7 ) × ( 7 × 7 ) = 7 4 . This is not equal to 7 6 .
7 6 is exactly what we have.
6 7 means 6 multiplied by itself 7 times, which is not equal to 7 6 .
6 × 7 = 42 , which is not equal to 7 6 .
Final Answer Therefore, the expression 7 × 7 × 7 × 7 × 7 × 7 is equal to 7 6 .
Examples
Exponents are a shorthand way of writing repeated multiplication. For example, if you are calculating the area of a square garden that has sides of length 7 meters, and you want to build a fence around it, you might need to calculate the area of the garden if you want to buy some fertilizer. If you then decide to expand the garden to be 7 meters by 7 meters, and then expand it again to be 7 meters by 7 meters, you can represent the final area as 7 × 7 × 7 × 7 × 7 × 7 = 7 6 square meters. This makes it easier to calculate and understand the size of the garden after multiple expansions.
