Question

directions - simplify the expression so all exponents are positive.
$b^{5}x^{-9}y^{7} = $

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) for any non - zero real number \(a\) and positive integer \(n\). In the expression \(b^{5}x^{-9}y^{7}\), we focus on the term with the negative exponent, which is \(x^{-9}\).

Step2: Apply the negative exponent rule

Using the rule \(a^{-n}=\frac{1}{a^{n}}\), we can rewrite \(x^{-9}\) as \(\frac{1}{x^{9}}\). So, when we substitute this back into the original expression \(b^{5}x^{-9}y^{7}\), we get \(b^{5}\times\frac{1}{x^{9}}\times y^{7}\).

Step3: Rewrite the expression

Multiplying the terms together, we can write the expression as \(\frac{b^{5}y^{7}}{x^{9}}\).

Answer:

\(\frac{b^{5}y^{7}}{x^{9}}\)