Question

simplify the exponential expression.
\\(\frac{30a^{4}b^{7}}{10ab^{9}}\\)
\\(\frac{30a^{4}b^{7}}{10ab^{9}} = \square\\)
(simplify your answer. type exponential notation with positive exponents.)

Explanation:

Step1: Simplify the coefficients

Divide 30 by 10: $\frac{30}{10} = 3$

Step2: Simplify the \(a\)-terms

Using the rule $\frac{a^m}{a^n} = a^{m - n}$, for \(a\)-terms: $\frac{a^4}{a^1} = a^{4 - 1} = a^3$

Step3: Simplify the \(b\)-terms

Using the rule $\frac{b^m}{b^n} = b^{m - n}$, for \(b\)-terms: $\frac{b^7}{b^9} = b^{7 - 9} = b^{-2}=\frac{1}{b^2}$ (but we need positive exponents, so we keep it as $\frac{1}{b^2}$ and combine with other terms)

Step4: Combine all simplified terms

Multiply the coefficient, \(a\)-term, and \(b\)-term: $3\times a^3\times\frac{1}{b^2}=\frac{3a^3}{b^2}$

Answer:

$\frac{3a^3}{b^2}$