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Which law would you use to simplify the expression [tex]\left(x^4\right)^9[/tex]?

A. Product of powers
B. Power of a product
C. Power of a quotient
D. Power of a power

Sagot :

GinnyAnswer
To simplify the expression \(\left(x^4\right)^9\), you should use the "power of a power" law.

Here's a detailed explanation:

1. Identify the law: The "power of a power" law states that \((a^m)^n = a^{m \cdot n}\). Essentially, when you raise an exponentiated term to another exponent, you multiply the exponents together.

2. Apply the law: In the expression \(\left(x^4\right)^9\), \(a = x\), \(m = 4\), and \(n = 9\).

3. Simplify the expression: Using the "power of a power" law, you can simplify \(\left(x^4\right)^9\) as follows:
[tex]\[ \left(x^4\right)^9 = x^{4 \cdot 9} = x^{36} \][/tex]

The law used here is the "power of a power" law.
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