(2p^2)^3 Without Exponents

Jasonbradley

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Jun 16, 2024

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Expanding (2p^2)^3 without Exponents

This problem involves simplifying an expression with exponents. Let's break it down step-by-step:

Understanding the problem:

• (2p^2)^3: This expression means we're multiplying the base (2p^2) by itself three times.

Applying the rules of exponents:

• (ab)^n = a^n * b^n: We distribute the exponent outside the parentheses to each factor inside.
• (a^m)^n = a^(m*n): When raising a power to another power, we multiply the exponents.

Step-by-step solution:

1. Apply the first rule: (2p^2)^3 = 2^3 * (p^2)^3
2. Apply the second rule: 2^3 * (p^2)^3 = 8 * p^(2*3)
3. Simplify: 8 * p^(2*3) = 8 * p^6

Therefore, (2p^2)^3 expanded without exponents is 8 * p^6.