Question

simplify. express your answer using positive exponents. \\(\frac{10a^{-6}b^{-5}c}{2a^{6}b^{6}c^{0}}\\)

Explanation:

Step1: Simplify the coefficient

Divide the coefficient 10 by 2: $\frac{10}{2} = 5$

Step2: Simplify the variable \(a\)

Using the rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \), for \(a\) we have \(a^{-6}\div a^{6}=a^{-6 - 6}=a^{-12}\). Since we need positive exponents, \(a^{-12}=\frac{1}{a^{12}}\)

Step3: Simplify the variable \(b\)

For \(b\), using the same exponent rule: \(b^{-3}\div b^{6}=b^{-3 - 6}=b^{-9}=\frac{1}{b^{9}}\)

Step4: Simplify the variable \(c\)

For \(c\), \(c\div c^{0}\) (note that \(c^{0} = 1\) for \(c
eq0\)), so \(c\div1 = c^{1-0}=c^{1}=c\)

Step5: Combine all parts

Multiply the simplified coefficient and variables together: \(5\times\frac{1}{a^{12}}\times\frac{1}{b^{9}}\times c=\frac{5c}{a^{12}b^{9}}\)

Answer:

\(\frac{5c}{a^{12}b^{9}}\)