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Chapter 0: Problem 29

Simplify each exponential expression. $$x^{-5} \cdot x^{10}$$

Short Answer

Expert verified
The simplified expression of \(x^{-5} \cdot x^{10}\) is \(x^5\).

Step by step solution

01

Understanding the Properties of Exponents

An important property of exponents states that for any non-zero number, \(a\) and any integers \(m\) and \(n\), \(a^m \cdot a^n = a^{m+n}\). Essentially, when multiplying two expressions with the same base, we keep the base and add the exponents.
02

Applying the Property

In this example, both expressions have the same base, \(x\). So, apply the property to simplify the expression: \(x^{-5} \cdot x^{10} = x^{-5 + 10}\).
03

Simplify the Exponent

Add the exponents together: \(x^{-5 + 10} = x^5\).

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Most popular questions from this chapter

Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)

Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{2 x+3 y}{x+1}, \text { for } x=-2 \text { and } y=4$$

Find the union of the sets. $$\\{0,1,3,5\\} \cup\\{2,4,6\\}$$

Using an example, explain how to factor out the greatest common factor of a polynomial.

Evaluate each algebraic expression for the given value or values of the variable(s). $$7+5 x, \text { for } x=10$$
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