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Write the following expression without negative exponents and without parentheses. (-3x)^(-2) Answer:

Write the following expression without negative exponents and without parentheses.\newline(−3x)−2 (-3 x)^{-2} \newlineAnswer:

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Full solution

Q. Write the following expression without negative exponents and without parentheses.\newline(−3x)−2 (-3 x)^{-2} \newlineAnswer:
  1. Understand Negative Exponents: Understand the properties of negative exponents. The negative exponent rule states that a−n=1ana^{-n} = \frac{1}{a^n} for any non-zero aa and positive integer nn. We will apply this rule to the expression (−3x)−2(-3x)^{-2}.
  2. Apply Negative Exponent Rule: Apply the negative exponent rule to the expression.\newlineUsing the rule from Step 11, we can rewrite (−3x)−2(-3x)^{-2} as 1((−3x)2)\frac{1}{((-3x)^2)}.
  3. Simplify Expression Inside Parentheses: Simplify the expression inside the parentheses.\newlineWhen we square (−3x)(-3x), we square both the coefficient and the variable. This gives us (−3)2×x2(-3)^2 \times x^2.
  4. Calculate Squares: Calculate the square of −3-3 and xx.(−3)2(-3)^2 equals 99 because the square of a negative number is positive. x2x^2 remains as it is. So, (−3)2×x2(-3)^2 \times x^2 becomes 9x29x^2.
  5. Write Final Expression: Write the final expression without negative exponents and without parentheses.\newlineThe final expression is 19x2\frac{1}{9x^2}.

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