Question

Rewrite the expression with positive exponents. $$\frac{1}{9 x^{-3} y^{-1}}$$

Short answer

\(9x^{3}y\)

Step-by-step solution

Apply the negative exponents rule

Start by applying the negative exponent rule to each part, this rule can be stated as \(a^{-n} = \frac{1}{a^n}\), where 'a' is the base number (which can be any kind of number or even an expression) and 'n' is the negative exponent (also called power). Our expression is \(\frac{1}{9 x^{-3} y^{-1}}\), thus simplifying each part of the expression using the said rule, we get \(\frac{1}{\frac{1}{9} \cdot \frac{1}{x^{3}} \cdot \frac{1}{y^{1}}}\)

Simplify the expression

Now, let's simplify the expression in the denominator. According to the rules of fractions, when a fraction is in the denominator of another fraction, it can be simplified by flipping it and changing the operation to multiplication at the same time. So we flip all fractions in the denominator and change division to multiplication: \(\frac{1}{9} \cdot x^{3} \cdot y^{1}\). Now multiply the fractions resulting in \(9x^{3}y\)

Finalize the answer

Because we have 1 at the numerator and \(9x^{3}y\) at the denominator, thus our final answer is simply: \(9x^{3}y\)