Question

1. $4^{-2x} cdot 4^{x} = 64$

Explanation:

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

\(4^{-2x} \cdot 4^{x}=4^{-2x + x}=4^{-x}\)

Step2: Rewrite 64 as a power of 4

Since \(4^3 = 64\), the equation becomes \(4^{-x}=4^3\)

Step3: Set exponents equal (if \(a^m = a^n\), then \(m = n\) for \(a>0,a

eq1\))
\(-x = 3\)

Step4: Solve for \(x\)

Multiply both sides by -1: \(x=- 3\)

Answer:

\(x = - 3\)