%5E4.jpeg "(7a^5b^6)^4")
Simplifying (7a^5b^6)^4
This expression involves raising a monomial to a power. To simplify this, we'll use the following rules of exponents:
- Product of powers: (x^m)^n = x^(m*n)
Let's break down the simplification:
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Apply the product of powers rule to the entire expression: (7a^5b^6)^4 = 7^4 * (a^5)^4 * (b^6)^4
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Simplify each term:
- 7^4 = 2401
- (a^5)^4 = a^(5*4) = a^20
- (b^6)^4 = b^(6*4) = b^24
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Combine the terms: 2401 * a^20 * b^24 = 2401a^20b^24
Therefore, the simplified form of (7a^5b^6)^4 is 2401a^20b^24.