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Simplify $\sqrt{2^{\left(2x-3\right)}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2x-3$ and $n$ equals $\frac{1}{2}$
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$2^{\frac{1}{2}\left(2x-3\right)}=4^{\left(x-1\right)}$
Learn how to solve problems step by step online. Solve the equation with radicals 2^(2x-3)^1/2=4^(x-1). Simplify \sqrt{2^{\left(2x-3\right)}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2x-3 and n equals \frac{1}{2}. Rewrite the power 4^{\left(x-1\right)} with base 2. Simplify \left(2^{2}\right)^{\left(x-1\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals x-1. If the bases are the same, then the exponents must be equal to each other.