Question

$a^{5}b^{4}\times\frac{1}{a^{2}b^{3}} = $
(a) $a^{7}b^{5}$
(b) $a^{3}b$
(c) $ab$
(d) $\frac{1}{a^{3}b}$
(e) $\frac{1}{a^{7}b^{7}}$

Explanation:

Step1: Recall exponent rule for division

When dividing terms with the same base, we subtract the exponents: \(x^m\div x^n = x^{m - n}\). Here, we have \(a^{4}b^{6}\times\frac{1}{a^{1}b^{5}}\), which is equivalent to \(a^{4}b^{6}\div(a^{1}b^{5})\).

Step2: Apply exponent rule to \(a\) terms

For the \(a\) terms: \(a^{4}\div a^{1}=a^{4 - 1}=a^{3}\).

Step3: Apply exponent rule to \(b\) terms

For the \(b\) terms: \(b^{6}\div b^{5}=b^{6 - 5}=b^{1}=b\).

Step4: Combine the results

Combining the results for \(a\) and \(b\) terms, we get \(a^{3}b\).

Answer:

B. \(a^{3}b\)