Which expression is equivalent to 6 6×3 6×6×6 6×6×6×6 3×3×3×3×3×3
The Correct Answer and Explanation is:
Of the options provided, the correct expression equivalent to 6³ is:
6 × 6 × 6
Explanation
The expression 6³ is a mathematical term written in exponential form. To understand which of the given choices is equivalent, it is essential to know the meaning of each part of this term. In an expression like aⁿ, ‘a’ is called the base, and ‘n’ is the exponent or power. The exponent indicates how many times the base number is to be multiplied by itself. Exponents provide a convenient shorthand for writing very long repeated multiplications.
In the case of 6³, the base is 6 and the exponent is 3. Following the rule of exponents, this expression means that the base, 6, must be multiplied by itself three times. Therefore, the expanded form of 6³ is 6 × 6 × 6. If you were to calculate the final value, you would first multiply 6 by 6 to get 36, and then multiply that result by 6 again, which equals 216.
Let’s analyze why the other options are incorrect.
- 6 × 3: This is a common mistake where the base is multiplied by the exponent. This is a simple multiplication problem that equals 18, which is not the same as 6³.
- 6 × 6 × 6 × 6: This expression shows the base, 6, being multiplied by itself four times. In exponential form, this would be written as 6⁴, not 6³.
- 3 × 3 × 3 × 3 × 3 × 3: This expression incorrectly reverses the roles of the base and the exponent. It shows the number 3 being multiplied by itself six times, which would be written in exponential form as 3⁶.
Based on this breakdown, the only expression that accurately represents the meaning of 6³ is the base number 6 multiplied by itself three times.thumb_upthumb_down
