Question

problem 17: tell whether these two expressions are equivalent. \\(\frac{5}{6x^3} \div \frac{5}{12x^5}\\) and \\(72x^8\\) after you pick your answer press go. yes no go

Explanation:

Step1: Recall division of fractions rule

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, \(\frac{5}{6z^3} \div \frac{5}{12z^5}=\frac{5}{6z^3}\times\frac{12z^5}{5}\)

Step2: Simplify the expression

Multiply the numerators and denominators: \(\frac{5\times12z^5}{6z^3\times5}\). The 5s cancel out. Then, \(\frac{12z^5}{6z^3}\). Divide 12 by 6 to get 2, and use the rule of exponents \(a^m\div a^n = a^{m - n}\) for \(z\): \(z^{5-3}=z^2\). So the simplified expression is \(2z^2\)

Step3: Compare with \(72z^8\)

\(2z^2\) is not equal to \(72z^8\) since the coefficients (2 vs 72) and the exponents of \(z\) (2 vs 8) are different.

Answer:

No