Question

Rewrite the expression using positive exponents. $$6 x^{-2} y^{-6}$$

Short answer

The expression \(6 x^{-2} y^{-6}\) rewritten with positive exponents is \(\frac{6}{x^{2}y^{6}}\).

Step-by-step solution

Recognize Negative Exponents

Recognize that there are negative exponents in the given expression, \(6 x^{-2} y^{-6}\). This means the terms \(x^{-2}\) and \(y^{-6}\) are reciprocals of \(x^{2}\) and \(y^{6}\) respectively.

Apply the Rule of Negative Exponents

Rewrite each term with the negative exponent in the denominator to create a new expression with positive exponents. This changes \(x^{-2}\) to \(\frac{1}{x^{2}}\) and \(y^{-6}\) to \(\frac{1}{y^{6}}\). The numerical coefficient, 6, remains as is.

Combine the Terms

Combining all the terms together, the expression becomes \(\frac{6}{x^{2}y^{6}}\).