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Chapter 2: Problem 34

Simplify. \(-\frac{11}{12}\left(\frac{3}{2} m^{3} n^{10}\right)^{2}\)

Short Answer

Expert verified
The simplified expression is \(-\frac{99}{48} m^6 n^{20}\).

Step by step solution

01

Distribute the exponent to both coefficients and variables

We need to raise the expression inside the parenthesis to the power of 2. To do this, distribute the exponent to both the coefficients and variables: \( \left( \frac{3}{2} m^{3} n^{10} \right)^{2} = \left( \frac{3^2}{2^2} \right) (m^{3 \cdot 2}) (n^{10 \cdot 2}) \)
02

Calculate the exponents and multiply fractions

Calculate the exponents for the coefficients and variables and multiply the fractions together: \( \left( \frac{3^2}{2^2} \right) (m^{6}) (n^{20}) = \frac{9}{4} m^6 n^{20} \) Now, we multiply the fractions: \( -\frac{11}{12} \cdot \frac{9}{4}m^6n^{20} \)
03

Simplify the expression

To simplify the expression, we need to multiply the coefficients and keep the variables as they are: \( -\frac{11}{12} \cdot \frac{9}{4} = -\frac{11 \cdot 9}{12 \cdot 4} = -\frac{99}{48}\) Combine the variables: \( m^{6} n^{20} \) Putting it all together gives us the simplified expression: \( -\frac{99}{48} m^6 n^{20} \)

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