what whole number is equivalent to the value of the expression \\(\\frac{5^8 \\cdot 5^6}{(5^4)^3}\\)? use…

what whole number is equivalent to the value of the expression \\(\\frac{5^8 \\cdot 5^6}{(5^4)^3}\\)? use the number pad to enter your answer in the box. the value of the expression is equivalent to the whole number \\(\\square\\).

what whole number is equivalent to the value of the expression \\(\\frac{5^8 \\cdot 5^6}{(5^4)^3}\\)? use the number pad to enter your answer in the box. the value of the expression is equivalent to the whole number \\(\\square\\).

Answer

Explanation:

Step1: Simplify numerator using exponent rule (a^m \cdot a^n = a^{m + n})

(5^8 \cdot 5^6 = 5^{8 + 6} = 5^{14})

Step2: Simplify denominator using exponent rule ((a^m)^n = a^{m \cdot n})

((5^4)^3 = 5^{4 \cdot 3} = 5^{12})

Step3: Simplify the fraction using exponent rule (\frac{a^m}{a^n} = a^{m - n})

(\frac{5^{14}}{5^{12}} = 5^{14 - 12} = 5^2)

Step4: Calculate (5^2)

(5^2 = 25)

Answer:

25