%5E3-without-exponents.jpeg "(2a^2)^3 Without Exponents")
Expanding (2a^2)^3 Without Exponents
The expression (2a^2)^3 involves exponents, but we can rewrite it without them using the properties of exponents.
Understanding the Properties
Here's a breakdown of the key properties we'll use:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Expanding the Expression
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Apply the power of a product rule: (2a^2)^3 = 2^3 * (a^2)^3
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Apply the power of a power rule: 2^3 * (a^2)^3 = 2^3 * a^(2*3)
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Simplify: 2^3 * a^(2*3) = 8a^6
Therefore, (2a^2)^3 expanded without exponents is 8a^6.
This process demonstrates how to break down expressions involving exponents into simpler forms using the fundamental rules of exponents.