Question 1: True or False?
To determine whether the work shown for simplifying the expression \((34)^{-3}\) is correct, we need to analyze the steps.
- The expression \((34)^{-3}\) simplifies to \(\frac{1}{(34)^3}\).
- The expression simplifies further to \(\frac{1}{34^3}\).
The work that's shown in the question seems incorrect. It appears that it involves manipulating the terms inappropriately, resulting in a nonsensical conclusion. Without seeing the complete steps, it is difficult to analyze fully, but the answer generally is:
False.
Question 2: Simplify the expression \((3p^3n^2)^4\):
To simplify this expression, we use the power of a product property and the power of a power property of exponents.
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Apply the exponent to each part of the product: \[ (3^4)(p^{3 \cdot 4})(n^{2 \cdot 4}) \]
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Calculate each part: \[ 3^4 = 81 \] \[ p^{3 \cdot 4} = p^{12} \] \[ n^{2 \cdot 4} = n^8 \]
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Combine the results: \[ 81p^{12}n^8 \]
Thus, the simplified expression is: \[ \boxed{81p^{12}n^8} \]
1 answer