%5E4(a%5E3)%5E3.jpeg "(2a^3)^4(a^3)^3")
Simplifying the Expression: (2a^3)^4(a^3)^3
This expression involves both exponents and parentheses, which require careful application of the rules of exponents. Let's break down the simplification process step-by-step:
1. Dealing with the Exponents Inside the Parentheses:
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(2a^3)^4: The exponent of 4 applies to both the coefficient (2) and the variable (a^3). This means we raise each of them to the fourth power:
- 2^4 = 16
- (a^3)^4 = a^(3*4) = a^12
- (2a^3)^4 = 16a^12
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(a^3)^3: Similarly, the exponent of 3 applies to the variable (a^3), resulting in:
- (a^3)^3 = a^(3*3) = a^9
2. Combining the Terms:
Now, our expression simplifies to: 16a^12 * a^9
3. Applying the Product of Powers Rule:
When multiplying exponents with the same base, we add their powers.
- 16a^12 * a^9 = 16a^(12+9) = 16a^21
Final Result:
The simplified form of the expression (2a^3)^4(a^3)^3 is 16a^21.