Chapter 5: Q2. (page 226)

Determine whether $x^{y} \cdot x^{z} = x^{y z}$ , is sometimes, always or never true. Explain.

Short Answer

Expert verified

The given expression is sometimes true for which the exponents terms $y = z = 2$ andalways truefor which the exponents terms $y z = y + z$ forall $\{y, z\} \in Z^{+}$ .

Step by step solution

Step 1. Write down the given information.

The given expression is $x^{y} \cdot x^{z} = x^{y z}$ .

Step 2. Explanation.

The given expression

$x^{y} \cdot x^{z} = x^{y z}$

is simplified as:

$\begin{array}{l} x^{y} \cdot x^{z} = x^{y z} .... (Given) \\ But, x^{y} \cdot x^{z} = x^{y + z} .... (∵ x^{m} \cdot x^{n} = x^{m + n}) \end{array}$

Therefore, the given expression

$x^{y} \cdot x^{z} = x^{y z}$

is not always true.

It $x^{y} \cdot x^{z} = x^{y z}$

will always be true when

$y z = y + z$

The expression

$x^{y} \cdot x^{z} = x^{y z}$

is sometimes true for

$y = z = 2$

Step 3. Conclusion.

The given expression is sometimes true for which the exponents terms $y = z = 2$ and always true for which the exponents terms $y z = y + z \forall {y, z} \in Z^{+}$ .

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Determine whether $x^{y} \cdot x^{z} = x^{y z}$ , is sometimes, always or never true. Explain.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Explanation.

Step 3. Conclusion.

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Determine whetherxy⋅xz=xyz , is sometimes, always or never true. Explain.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Explanation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Determine whether $x^{y} \cdot x^{z} = x^{y z}$ , is sometimes, always or never true. Explain.