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Simplify. Assume that no denominator is equal to zero. \( \begin{array}{ll}\text { a. }\left(\frac{3 a}{a^{2}}\right)^{0} \\ \text { ac. }^{2} & \text { Ob. }\left(\frac{3}{a}\right)\end{array} \) Od. \( \frac{1}{a} \)

Ask by Matthews Young. in Saudi Arabia
Jan 21,2025

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Answer

a. \( 1 \) b. \( \frac{3}{a} \) c. \( \frac{1}{a} \)

Solution

Simplify the expression by following steps: - step0: Solution: \(\frac{3}{a}\) Calculate or simplify the expression \( \frac{1}{a} \). Simplify the expression by following steps: - step0: Solution: \(\frac{1}{a}\) Calculate or simplify the expression \( 1/a \). Simplify the expression by following steps: - step0: Solution: \(\frac{1}{a}\) Calculate or simplify the expression \( 3/a \). Simplify the expression by following steps: - step0: Solution: \(\frac{3}{a}\) Calculate or simplify the expression \( (3*a)/(a^2) \). Simplify the expression by following steps: - step0: Solution: \(\frac{3a}{a^{2}}\) - step1: Simplify the expression: \(\frac{3}{a^{2-1}}\) - step2: Calculate: \(\frac{3}{a}\) Let's simplify each expression step by step. ### a. Simplifying \( \left(\frac{3 a}{a^{2}}\right)^{0} \) According to the properties of exponents, any non-zero expression raised to the power of 0 is equal to 1. Therefore: \[ \left(\frac{3 a}{a^{2}}\right)^{0} = 1 \] ### b. Simplifying \( \frac{3}{a} \) This expression is already in its simplest form: \[ \frac{3}{a} \] ### c. Simplifying \( \frac{1}{a} \) This expression is also in its simplest form: \[ \frac{1}{a} \] ### Summary of Results - a. \( \left(\frac{3 a}{a^{2}}\right)^{0} = 1 \) - b. \( \frac{3}{a} \) - c. \( \frac{1}{a} \) Thus, the simplified forms are: - a: \( 1 \) - b: \( \frac{3}{a} \) - c: \( \frac{1}{a} \)

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Mind Expander

Anything raised to the power of zero is equal to one, as long as the base is not zero. So, for \(\left(\frac{3 a}{a^{2}}\right)^{0}\), the result is simply \(1\). This holds true regardless of the value of \(a\), provided \(a \neq 0\). On the other hand, simplifying \(\left(\frac{3}{a}\right)\) leads to the expression \(\frac{3}{a}\), which is a perfectly valid representation of the fraction that describes the relationship of 3 to \(a\). If you were to combine this with \(\frac{1}{a}\), you could factor multiples or perform operations depending on the context, but each stands as solid expressions in their own right!

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