which expression is equivalent to $left(2^{\frac{1}{2}}cdot2^{\frac{3}{4}}\right)^2$?\n$sqrt4{2^{3}}$\n$sqrt{…

which expression is equivalent to $left(2^{\frac{1}{2}}cdot2^{\frac{3}{4}}\right)^2$?\n$sqrt4{2^{3}}$\n$sqrt{2^{5}}$\n$sqrt4{4^{3}}$\n$sqrt{4^{5}}$

which expression is equivalent to $left(2^{\frac{1}{2}}cdot2^{\frac{3}{4}}\right)^2$?\n$sqrt4{2^{3}}$\n$sqrt{2^{5}}$\n$sqrt4{4^{3}}$\n$sqrt{4^{5}}$

Answer

Explanation:

Step1: Use exponent - product rule

When multiplying two numbers with the same base (a^m\cdot a^n=a^{m + n}), so (2^{\frac{1}{2}}\cdot2^{\frac{3}{4}}=2^{\frac{1}{2}+\frac{3}{4}}). (2^{\frac{1}{2}+\frac{3}{4}}=2^{\frac{2 + 3}{4}}=2^{\frac{5}{4}})

Step2: Apply power - of - a - power rule

((2^{\frac{5}{4}})^2=2^{\frac{5}{4}\times2}) (2^{\frac{5}{4}\times2}=2^{\frac{5}{2}})

Step3: Rewrite in radical form

(2^{\frac{5}{2}}=\sqrt{2^{5}})

Answer:

(\sqrt{2^{5}})