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Chapter 2: Problem 26

Simplify. \(\frac{\left(-5 m^{7}\right)^{3}}{\left(5 n^{12}\right)^{2}}\)

Short Answer

Expert verified
\(-5 m^{21} n^{-24}\)

Step by step solution

01

Apply the rule for powers of products

We will apply the rule for powers of products to the given expression. This means that we will raise each term inside the parenthesis to the given power. Given expression: \( \frac{(-5 m^7)^3}{(5 n^{12})^2} \) Applying the rule for powers of products: In the numerator: \((-5)^3(m^7)^3 = -125 m^{21}\) In the denominator: \((5)^2(n^{12})^2 = 25 n^{24}\) Now the expression becomes: \(\frac{-125 m^{21}}{25 n^{24}}\)
02

Apply the rule for powers of quotients

Now we will apply the rule for powers of quotients: Expression: \(\frac{-125 m^{21}}{25 n^{24}} = -5^3 m^{21} * 5^{-2} n^{-24}\)
03

Simplify the expression

Combine the constants with the same base: \(-5^3 * 5^{-2} = -5^{(3-2)} = -5^1 = -5\) Now, our simplified expression is: \(-5 m^{21} n^{-24}\)

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