Questions: 4 x^(-4)(x^4)^4 x^(-1)

4 x^(-4)(x^4)^4 x^(-1)
Transcript text: $4 x^{(-4)}\left(x^{4}\right)^{4} x^{(-1)}$
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Solution

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Solution Steps

To simplify the expression \(4 x^{(-4)}\left(x^{4}\right)^{4} x^{(-1)}\), we can use the properties of exponents. First, apply the power of a power rule to \(\left(x^{4}\right)^{4}\), which is \(x^{16}\). Then, combine all the exponents of \(x\) by adding them together: \(-4 + 16 - 1\). Finally, simplify the expression using the calculated exponent.

Step 1: Apply the Power of a Power Rule

To simplify the expression \(4 x^{(-4)}\left(x^{4}\right)^{4} x^{(-1)}\), we first apply the power of a power rule to \(\left(x^{4}\right)^{4}\). According to this rule, \(\left(x^{a}\right)^{b} = x^{a \cdot b}\). Therefore, \(\left(x^{4}\right)^{4} = x^{16}\).

Step 2: Combine the Exponents

Next, we combine all the exponents of \(x\) in the expression \(4 x^{(-4)} x^{16} x^{(-1)}\). The exponents are \(-4\), \(16\), and \(-1\). We add these exponents together: \[ -4 + 16 - 1 = 11 \]

Step 3: Simplify the Expression

The expression now becomes \(4 x^{11}\), as we have combined the exponents into a single exponent of \(11\).

Final Answer

\(\boxed{4x^{11}}\)

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