Simplify the Expression: 5^-3 × 5^0 × 5^2 × 5^5 Using Laws of Exponents

Any number to the power of 0 equals 1. So $5^0 = 1$. This is a fundamental rule in mathematics - it doesn't matter if the base is 5, 10, or 100!

Treat negative exponents just like negative numbers in addition. So -3 + 0 + 2 + 5 becomes: -3 + 2 + 5 = 4 (the zero doesn't change anything).

The rule $a^m \cdot a^n = a^{m+n}$ comes from the definition of exponents. When you multiply $5^2 \cdot 5^3$, you're really doing (5×5) × (5×5×5), which gives you 5 multiplied by itself 5 times total!

No! This rule only works when the bases are identical. You cannot simplify $3^2 \cdot 5^4$ using exponent rules - the bases must be the same.

The same rule applies! Just add all the exponents together, no matter how many terms you have. For example: $a^2 \cdot a^3 \cdot a^{-1} \cdot a^5 \cdot a^0 = a^{2+3-1+5+0} = a^9$.

Calculate both sides numerically when possible. For this problem: $5^4 = 625$. You can also verify by calculating $\frac{1}{5^3} \cdot 1 \cdot 5^2 \cdot 5^5 = \frac{1}{125} \cdot 25 \cdot 3125 = 625$ ✓