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Chapter 5: Problem 11

Simplify each expression using the power rule. $$\left(x^{15}\right)^{3}$$

Short Answer

Expert verified
\((x^{15})^{3} = x^{45}\)

Step by step solution

01

Identify the bases and exponents

In the expression \((x^{15})^{3}\), the base, \(a\), is \(x\), the first exponent, \(m\), is 15, and the second exponent, \(n\), is 3.
02

Apply the power rule

Now that you have identified the base and exponents, you can apply the power rule, which is \((a^m)^n = a^{mn}\). This means you multiply the exponents together.
03

Perform the multiplication

Following from step two, you multiply 15 by 3, giving a total of 45. Therefore, \((x^{15})^{3} = x^{45}\).

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Most popular questions from this chapter

Explain how to convert from decimal to scientific notation and give an example.

How do you know if an exponential expression is simplified?

Describe one advantage of expressing a number in scientific notation over decimal notation.

In each exercise, find the product. $$9 x y\left(3 x y^{2}-y+9\right)$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\left(4 \times 10^{3}\right)+\left(3 \times 10^{2}\right)=4.3 \times 10^{3}$$
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