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Chapter 0: Problem 55

Simplify each exponential expression. $$\left(4 x^{3}\right)^{-2}$$

Short Answer

Expert verified
The simplified form of \( (4x^{3})^{-2} \) is \( \frac{1}{16x^{6}} \).

Step by step solution

01

Apply negative exponent rule

The negative exponent indicates a reciprocal. Therefore, rewrite \( (4x^{3})^{-2} \) as \( \frac{1}{(4x^{3})^{2}} \).
02

Apply power of a power rule

The power of a power rule states that when raising a power to a power, the exponents should be multiplied. Therefore, you multiply the exponent '3' of \( x \) by the outer exponent '2' to get \( \frac{1}{4^{2}x^{3 \cdot 2}} \).
03

Simplify result

Now calculate and simplify your expression. \(\frac{1}{4^{2}}\) becomes \(\frac{1}{16}\). \(x^{3 \cdot 2}\) becomes \(x^{6}\). Therefore, the simplified expression is \( \frac{1}{16x^{6}} \).

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Most popular questions from this chapter

Evaluate each algebraic expression for the given value or values of the variable(s). $$6+5(x-6)^{3}, \text { for } x=8$$

What does it mean to factor completely?

Find the intersection of the sets. $$\\{a, b, c, d\\} \cap \varnothing$$

$$\text { factor completely.}$$ $$-x^{2}-4 x+5$$

$$\text { factor completely.}$$ $$-x^{2}-4 x+5$$
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