Write $3 \times 3 \times 3 \times 3 \times 3 \times 3$ using exponents.
A. $9^4$
B. $6^3$
C. $12^3$
D. $3^6$
Answer (1)
The problem requires rewriting the expression 3 × 3 × 3 × 3 × 3 × 3 using exponents.
Recognize that repeated multiplication can be expressed using exponents.
Rewrite the expression as 3 6 .
Compare the result with the given options.
The correct option is 3 6 .
Explanation
Understanding the problem We are asked to write the expression 3 × 3 × 3 × 3 × 3 × 3 using exponents and choose the correct option from the given choices.
Writing with exponents The expression 3 × 3 × 3 × 3 × 3 × 3 means that the number 3 is multiplied by itself 6 times. This can be written as 3 6 , where 3 is the base and 6 is the exponent.
Comparing with options Now, let's compare 3 6 with the given options: A. 9 4 = 9 × 9 × 9 × 9 = 6561 B. 6 3 = 6 × 6 × 6 = 216 C. 1 2 3 = 12 × 12 × 12 = 1728 D. 3 6 = 3 × 3 × 3 × 3 × 3 × 3 = 729
Finding the correct option The expression 3 × 3 × 3 × 3 × 3 × 3 is equal to 3 6 , which is 729. Option D, 3 6 , matches this result.
Examples
Exponents are a shorthand way of writing repeated multiplication. For example, if you are calculating the area of a square garden that is 5 meters on each side, you would multiply 5 by itself: 5 × 5 . Using exponents, you can write this as 5 2 , which is read as '5 squared' and equals 25 square meters. This makes it easier to express and calculate areas and volumes, especially when dealing with larger numbers or more complex shapes.
