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Chapter 0: Problem 44

Simplify each exponential expression. $$\left(-3 x^{4} y^{6}\right)^{3}$$

Short Answer

Expert verified
The simplified exponential expression is \(-27x^{12}y^{18}\)

Step by step solution

01

Identify the expression

The expression given is \(\left(-3x^{4}y^{6}\right)^{3}\). This expression means -3 raised to the third power, x to the power of 4 raised to the third power, and y to the power of 6 raised to the third power.
02

Apply exponentiation rules

We know that when raising a power to another power, we multiply the exponents. Applying this rule, we get \(-3^{3}(x^{4*3})(y^{6*3}) = -3^{3}x^{12}y^{18}\)
03

Evaluate the exponential expression

Now evaluate \(-3^{3}\) which is \(-27\). The equation simplifies to \(-27x^{12}y^{18}\)

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Most popular questions from this chapter

Find the intersection of the sets. $$\\{1,3,7\\} \cap(2,3,8)$$

Rewrite each expression without absolute value bars. $$|-203|$$

Determine whether each statement in Exercises 43鈥�50 is true or false. $$0 \geq-13$$

$$\text { factor completely.}$$ $$x^{2 n}+6 x^{n}+8$$

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. \(\sqrt{7}+\sqrt{18} \quad \sqrt{7+18}\)
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