%5E3.jpeg "(2ab^5)^3")
Simplifying (2ab^5)^3
In mathematics, simplifying expressions is an important skill. One common type of expression involves raising a product to a power. Let's take a look at how to simplify the expression (2ab^5)^3.
Understanding the Properties of Exponents
To simplify this expression, we need to use the following properties of exponents:
- Product of powers: (a^m)^n = a^(m*n)
- Power of a product: (ab)^n = a^n * b^n
Simplifying the Expression
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Apply the power of a product property: (2ab^5)^3 = 2^3 * a^3 * (b^5)^3
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Apply the product of powers property: 2^3 * a^3 * (b^5)^3 = 2^3 * a^3 * b^(5*3)
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Simplify the exponents: 2^3 * a^3 * b^(5*3) = 8a^3b^15
The Final Result
Therefore, the simplified form of (2ab^5)^3 is 8a^3b^15.