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

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

Solution

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 $11$.