(5a%5E3b%5E8).jpeg "(3a^2b^7)(5a^3b^8)")
Simplifying Expressions with Exponents: (3a^2b^7)(5a^3b^8)
In mathematics, we often encounter expressions with exponents. These exponents represent repeated multiplication of a base number. To simplify expressions with exponents, we use the rules of exponents. Let's explore the simplification of the expression (3a^2b^7)(5a^3b^8).
Understanding the Rules of Exponents
Before we begin simplifying, let's recall some key rules:
- Product of powers: When multiplying terms with the same base, we add the exponents. For example: a^m * a^n = a^(m+n)
- Commutative Property of Multiplication: The order of multiplication doesn't matter. For example: a * b = b * a
Simplifying the Expression
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Rearrange the terms: Using the commutative property, we can rearrange the expression to group similar terms together: (3 * 5) * (a^2 * a^3) * (b^7 * b^8)
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Apply the product of powers rule:
- 3 * 5 = 15
- a^2 * a^3 = a^(2+3) = a^5
- b^7 * b^8 = b^(7+8) = b^15
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Combine the simplified terms: 15 * a^5 * b^15 = 15a^5b^15
Therefore, the simplified form of the expression (3a^2b^7)(5a^3b^8) is 15a^5b^15.