Evaluate \( y=\left(\frac{1}{5}\right)^{x} \), when \( x=0 \) \( y=\frac{1}{5} \quad y=1 \quad y=0 \)

To evaluate \( y=\left(\frac{1}{5}\right)^{x} \) when \( x=0 \), we substitute \( 0 \) for \( x \): \[ y=\left(\frac{1}{5}\right)^{0} \] Any number raised to the power of zero equals 1. Therefore, \[ y=1 \] So, the correct answer is \( y=1 \). Now, here's a fun fact: This principle holds true for any non-zero number. It’s like a magical rule in mathematics that brings a bit of consistency to the otherwise wild world of exponents! Additionally, you might wonder why this rule applies. It comes from the properties of exponents: dividing powers of the same base leads to subtracting their exponents according to the formula \( a^{m}/a^{n}=a^{m-n} \). So, if \( m=n \), you’d get \( a^{0}=1 \). It's a neat way to see the harmony in mathematical laws!