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Question

Write the expression (x^4)^8 in simplest form.

Asked By MidnightMystic28 at

Answered By Expert

Benjamin

Expert · 5.9k answers · 5k people helped

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Solution By Steps

Step 1: Apply the Power of a Power Rule

When raising a power to another power, multiply the exponents.

(x^4)^8 = x^{4 imes 8}

Step 2: Simplify the Exponent

Calculate the exponent:

4 imes 8 = 32.

Final Answer

(x^4)^8 = x^{32}

Summary:

The expression

(x^4)^8 simplifies to

x^{32} using the power of a power rule. This rule states that when raising a power to another power, you multiply the exponents. Understanding this rule is crucial in simplifying expressions involving exponents efficiently. In real-world applications, this concept is fundamental in various fields such as mathematics, physics, and engineering where complex calculations involving exponents are common.