134k views
4 votes
Simplify ((-3)^2)^3. Choose the correct answer:

A) (-3)^(2/3)
B) (-3)^(3/2)
C) (-3)^6
D) (-3)

1 Answer

4 votes

Final answer:

To simplify ((-3)^2)^3, we raise -3 to the 2nd power and then take that result and raise it to the 3rd power, effectively multiplying the exponents, resulting in (-3)^6 or 729. The correct answer is option C) (-3)^6.

Step-by-step explanation:

The question asks to simplify the expression ((-3)^2)^3. To simplify such expressions, you need to follow the rules of exponents. When you raise a power to another power, you multiply the exponents. In this case, we have (-3) squared, which is (-3)^2, being cubed, which means we multiply the exponent 2 by 3.

Here's the step-by-step process:

  1. Start with the innermost parentheses, (-3)^2, which means -3 multiplied by itself: -3 × -3 = 9.
  2. Now take this result, which is 9, and raise it to the power of 3 since the original expression was ((-3)^2)^3. So we have (9)^3.
  3. 9 cubed is 9 × 9 × 9 = 729. Therefore, the expression simplifies to 729.

However, if we approach this problem using the exponent multiplication rule and treat the expression as a power of a power, we get:

(((-3)^2)^3 = (-3)^(2×3) = (-3)^6).

Since -3 raised to an even power is always positive, the answer is still 729. Hence the correct answer is option C) ((-3)^6).

User Utkarsh Sinha
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories