Q. Write the following expression without negative exponents and without parentheses.(−5x)−3Answer:
Understand Negative Exponents: Understand the properties of negative exponents. The negative exponent rule states that a−n=an1 for any non-zero a and positive integer n. We will apply this rule to the expression (−5x)−3.
Apply Negative Exponent Rule: Apply the negative exponent rule to the expression.Using the rule from Step 1, we can rewrite (−5x)−3 as ((−5x)3)1.
Expand Denominator: Expand the expression in the denominator.Now we need to raise (−5x) to the power of 3. This means we will multiply −5x by itself three times: (−5x)×(−5x)×(−5x).
Calculate Denominator: Calculate the expression in the denominator.(−5x)×(−5x)×(−5x)=−5×−5×−5×x×x×x=125x3 because a negative number multiplied by itself an odd number of times remains negative, and x multiplied by itself three times is x3.
Write Final Expression: Write the final expression without negative exponents and without parentheses.The final expression is 125x31.