\( \left(\frac{0.8}{2.6}\right)^{4} \quad \begin{array}{l}\text { - Quotient of Powers Law } \\ \text { - Power of a Quotient Law } \\ \text { - Zero Exponent Law }\end{array} \)

To simplify the expression \( \left(\frac{0.8}{2.6}\right)^{4} \), we can apply the **Power of a Quotient Law**. This law states that: \[ \left(\frac{a}{b}\right)^{n} = \frac{a^{n}}{b^{n}} \] In this case, we can let \( a = 0.8 \), \( b = 2.6 \), and \( n = 4 \). Applying the law, we get: \[ \left(\frac{0.8}{2.6}\right)^{4} = \frac{0.8^{4}}{2.6^{4}} \] Now, we can calculate \( 0.8^{4} \) and \( 2.6^{4} \): 1. Calculate \( 0.8^{4} \): \[ 0.8^{4} = (0.8 \times 0.8 \times 0.8 \times 0.8) = 0.4096 \] 2. Calculate \( 2.6^{4} \): \[ 2.6^{4} = (2.6 \times 2.6 \times 2.6 \times 2.6) = 45.6976 \] Now, substituting these values back into the expression gives us: \[ \left(\frac{0.8}{2.6}\right)^{4} = \frac{0.4096}{45.6976} \] Finally, we can compute this division: \[ \frac{0.4096}{45.6976} \approx 0.00896 \] Thus, the simplified expression is: \[ \left(\frac{0.8}{2.6}\right)^{4} \approx 0.00896 \] In summary, we used the **Power of a Quotient Law** to simplify the expression.