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Chapter 0: Problem 46

Simplify each exponential expression. $$\left(11 x^{5}\right)\left(9 x^{12}\right)$$

Short Answer

Expert verified
The simplified form of the given exponential expression is \(99x^{17}\).

Step by step solution

01

Observe the Expression

Look at the expression: \( (11x^{5})(9x^{12}) \). It consists of two parts: coefficients (11 and 9) and exponential terms (\(x^{5}\) and \(x^{12}\)). These parts need to be handled separately.
02

Multiply the Coefficients

Multiply the coefficients: \(11 \times 9 = 99\). This will be the new coefficient on the \(x\) variable.
03

Add Exponents

When multiplying exponential expressions with the same base, we add the exponents together, as stipulated by the law of exponents. So, do \(5 + 12 = 17\) to add the two exponents of \(x\).
04

Write down the Final Solution

Combine the results of steps 2 and 3 to form the final solution: \(99x^{17}\). This is the simplest form the original expression can be written in.

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Most popular questions from this chapter

Evaluate each algebraic expression for the given value or values of the variable(s). $$4+5(x-7)^{3}, \text { for } x=9$$

a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$\text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. }$$ How old is the son? b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?

What does it mean to factor completely?

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List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. $$\\{-7,-0 . \overline{6}, 0, \sqrt{49}, \sqrt{50}\\}$$
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