Chapter 5: Problem 3

Simplify each of the following: (a) \(\frac{a^{11}}{a^{4}}\) (b) \(\left(a^{b}\right)^{4}\)

Short Answer

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Question: Simplify the following expressions: (a) \(\frac{a^{11}}{a^{4}}\) (b) \(\left(a^{b}\right)^{4}\) Answer: (a) \(a^{7}\) (b) \(a^{4b}\)

Step by step solution

Apply the quotient rule in (a)

First, simplify the expression \(\frac{a^{11}}{a^{4}}\). To simplify this expression, we will apply the quotient rule, which states that \(a^{m-n} = \frac{a^m}{a^n}\). Therefore in our case, we have \(a^{11-4} = \frac{a^{11}}{a^{4}}\). So, the simplified expression is \(a^{7}\).

Apply the power of a power rule in (b)

Next, simplify the expression \(\left(a^{b}\right)^{4}\). To simplify this expression, we will apply the power of a power rule, which states that \((a^m)^n=a^{mn}\). Therefore, in our case, we have \(a^{b\cdot 4}=\left(a^b\right)^4\). So, the simplified expression is \(a^{4b}\). The simplified expressions for the given exercise are: (a) \(a^{7}\) (b) \(a^{4b}\)

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Simplify each of the following: (a) \(\frac{a^{11}}{a^{4}}\) (b) \(\left(a^{b}\right)^{4}\)

Short Answer

Step by step solution

Apply the quotient rule in (a)

Apply the power of a power rule in (b)

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