Question

5.1 exponent p
(1 point)
divide using the quotient rule:
\frac{25 a^{17} b^{14}}{5 a b^{12}}=\square
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Explanation:

Step1: Divide the coefficients

The coefficient of the numerator is \(25\) and the coefficient of the denominator is \(5\). Using the rule \(\frac{a}{b}\) (where \(a = 25\) and \(b=5\)), we have \(\frac{25}{5}=5\).

Step2: Apply the quotient rule for exponents on \(a\) - terms

For the \(a\) - terms, we use the quotient rule \(x^{m}\div x^{n}=x^{m - n}\). Here, \(m = 17\) and \(n = 1\) (since \(a=a^{1}\)), so \(a^{17}\div a^{1}=a^{17 - 1}=a^{16}\).

Step3: Apply the quotient rule for exponents on \(b\) - terms

For the \(b\) - terms, using the quotient rule \(x^{m}\div x^{n}=x^{m - n}\), with \(m = 14\) and \(n = 12\), we get \(b^{14}\div b^{12}=b^{14 - 12}=b^{2}\).

Answer:

\(5a^{16}b^{2}\)