(25b^6)^-1.5

Jasonbradley

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Jun 16, 2024

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Simplifying (25b^6)^-1.5

This problem involves simplifying an expression with exponents. Let's break it down step by step:

Understanding the Properties of Exponents

We'll use the following properties of exponents:

• Product of powers: (x^m)^n = x^(m*n)
• Negative exponent: x^-n = 1/x^n

Applying the Properties

1. Simplify the exponent: -1.5 = -3/2
2. Apply the product of powers rule: (25b^6)^(-3/2) = 25^(-3/2) * (b^6)^(-3/2)
3. Simplify the exponents: 25^(-3/2) * (b^6)^(-3/2) = 25^(-3/2) * b^(-18/2)
4. Simplify the exponents further: 25^(-3/2) * b^(-18/2) = 25^(-3/2) * b^(-9)
5. Apply the negative exponent rule: 25^(-3/2) * b^(-9) = 1/25^(3/2) * 1/b^9
6. Simplify the base: 1/25^(3/2) * 1/b^9 = 1/(5^2)^(3/2) * 1/b^9 = 1/5^3 * 1/b^9
7. Calculate the final result: 1/5^3 * 1/b^9 = 1/125 * 1/b^9 = 1/(125b^9)

Final Answer

Therefore, the simplified form of (25b^6)^-1.5 is 1/(125b^9).