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Chapter 0: Problem 40

Simplify each exponential expression. $$\left(6 x^{4}\right)^{2}$$

Short Answer

Expert verified
The simplified form of the expression is \(36x^8\).

Step by step solution

01

Identify base and exponent

In the expression \((6 x^{4})^{2}\), we have a base of \(6x^4\) and an exponent of 2.
02

Distribute the outer exponent to each part of the base

Using the laws of exponents, we can distribute the outer exponent of 2 to both the 6 and the \(x^4\) to get \((6^2)(x^{4*2})\).
03

Simplify powers

We know that \(6^2 = 36\) and \(x^8 = x^8\). Therefore \((6^2)(x^{4*2})\) simplifies to \(36x^8\).

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Most popular questions from this chapter

Fill in each box to make the statement true. Place the correct symbol, \(>\) or \(<,\) in the shaded area between the given numbers. Do not use a calculator. Then check your result with a calculator. a. \(3^{\frac{1}{2}} 3^{\frac{1}{3}}\) b. \(\sqrt{7}+\sqrt{18} \quad \sqrt{7+18}\)

Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{7(x-3)}{2 x-16}, \text { for } x=9$$

Determine whether each statement in Exercises 43鈥�50 is true or false. $$-13 \leq-2$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$8^{-\frac{1}{3}}=-2$$

Factor and simplify each algebraic expression. $$(4 x-1)^{\frac{1}{2}}-\frac{1}{3}(4 x-1)^{\frac{3}{2}}$$
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