Question

which product is equal to $5^6$? $5^2\cdot5^3$ $5^7\cdot5^1$ $5^3\cdot5^3$ $5^8\cdot5^2$

Explanation:

Step1: Recall exponent product rule

For same base $a$, $a^m \cdot a^n = a^{m+n}$

Step2: Calculate each option

• Option1: $5^2 \cdot 5^3 = 5^{2+3}=5^5$
• Option2: $5^7 \cdot 5^1 = 5^{7+1}=5^8$
• Option3: $5^3 \cdot 5^3 = 5^{3+3}=5^6$
• Option4: $5^8 \cdot 5^2 = 5^{8+2}=5^{10}$

Answer:

$5^3 \cdot 5^3$