Question

what is the va\\(\frac{5^4 \times 5^4 \times 5^{-2}}{5^3 \times 5^{-6}}\\)

Explanation:

Step1: Use exponent rule \(a^m \times a^n = a^{m + n}\) on numerator and denominator.

Numerator: \(5^{4} \times 5^{4} \times 5^{-2}=5^{4 + 4+(-2)} = 5^{6}\)
Denominator: \(5^{3} \times 5^{-6}=5^{3+(-6)} = 5^{-3}\)

Step2: Use exponent rule \(\frac{a^m}{a^n}=a^{m - n}\)

\(\frac{5^{6}}{5^{-3}} = 5^{6-(-3)}=5^{9}\)

Step3: Calculate \(5^{9}\)

\(5^{9}=5\times5\times5\times5\times5\times5\times5\times5\times5 = 1953125\)

Answer:

\(1953125\)