Problem 28
Question
Simplify each exponential expression. $$x^{11} \cdot x^{5}$$
Step-by-Step Solution
Verified Answer
The simplified form of the given expression is \(x^{16}\)
1Step 1: Identify the base and exponents
In the expression \(x^{11} \cdot x^{5}\), the base is \(x\) and the exponents are \(11\) and \(5\) respectively.
2Step 2: Apply the Product of Powers Property
According to the Product of Powers Property, the exponents are added while the base remains the same. This gives: \(x^{11+5}\)
3Step 3: Simplify the exponent
Add the exponents together i.e. \(11+5=16\). So, the simplified expression becomes: \(x^{16}\)
Other exercises in this chapter
Problem 27
Use the quotient rule to simplify the expressions in Exercises \(23-32\) Assume that \(x>0\) $$\frac{\sqrt{48 x^{3}}}{\sqrt{3 x}}$$
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Find the intersection of the sets. $$\\{w, y, z\\} \cap \varnothing$$
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Factor each trinomial, or state that the trinomial is prime. $$6 x^{2}-17 x+12$$
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Multiply or divide as indicated. $$\frac{x^{2}+x}{x^{2}-4} \div \frac{x^{2}-1}{x^{2}+5 x+6}$$
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