Moreno Luna
07/04/2024 · Primary School

Question 1 Use exponent rules to simplify the following, giving all answers with positive exponents. (a) \( 6^{3} \times 6^{-5} \times 6^{-2} \)

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To simplify the expression \( 6^{3} \times 6^{-5} \times 6^{-2} \), we can use the exponent rule that states \( a^m \times a^n = a^{m+n} \). 1. First, we add the exponents: \[ 3 + (-5) + (-2) = 3 - 5 - 2 = 3 - 7 = -4 \] 2. Now we can rewrite the expression using the sum of the exponents: \[ 6^{3} \times 6^{-5} \times 6^{-2} = 6^{-4} \] 3. To express this with positive exponents, we use the rule \( a^{-n} = \frac{1}{a^n} \): \[ 6^{-4} = \frac{1}{6^{4}} \] Thus, the simplified expression with positive exponents is: \[ \frac{1}{6^{4}} \]

Quick Answer

\[ \frac{1}{6^{4}} \]
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