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Chapter 5: Problem 10

Simplify each expression using the power rule. $$\left(6^{7}\right)^{10}$$

Short Answer

Expert verified
The simplified expression is \(6^{70}\).

Step by step solution

01

Identify the base and the exponents

In this case, the base is 6, the first exponent is 7 and the second exponent, which is our power to the power, is 10. The expression can be written as \(6^{7^{10}}\).
02

Apply the Power Rule

According to the power rule, when we raise a power to another power, we multiply the exponents. So by the power rule, \(6^{7^{10}} = 6^{7*10}\).
03

Simplify the expression

Now, simply multiply the exponents. The exponent is \(7*10 = 70\). So, the final, simplified expression is \(6^{70}\).

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Most popular questions from this chapter

Explain the negative exponent rule and give an example.

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