Question

evaluate the following expression. enter each answer as an integer or a simplified fraction.\\(\frac{6y^{-2}}{5x^{-1}}\\)\
your answer can be simplified further.\
thats not it. try again. score: 0%

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) (where \(a
eq0\) and \(n\) is a positive integer). So we can rewrite \(y^{-2}\) as \(\frac{1}{y^{2}}\) and \(x^{-1}\) as \(\frac{1}{x}\), but when dealing with fractions, a negative exponent in the numerator moves to the denominator and becomes positive, and a negative exponent in the denominator moves to the numerator and becomes positive. So for \(\frac{6y^{-2}}{5x^{-1}}\), we can move \(y^{-2}\) to the denominator (becoming \(y^{2}\)) and \(x^{-1}\) to the numerator (becoming \(x^{1}=x\)).

Step2: Apply the rule to the expression

Applying the negative exponent rule to \(\frac{6y^{-2}}{5x^{-1}}\), we get \(\frac{6x}{5y^{2}}\).

Answer:

\(\frac{6x}{5y^{2}}\)