which is equivalent to $\frac{2^{0}2^{3}}{sqrt{2}}$?\na. 0\nb. $sqrt5{2^{2}}$\nc. $sqrt{2^{5}}$\nd…

which is equivalent to $\frac{2^{0}2^{3}}{sqrt{2}}$?\na. 0\nb. $sqrt5{2^{2}}$\nc. $sqrt{2^{5}}$\nd. $sqrt3{2^{2}}$\ne. $sqrt{2^{3}}$

which is equivalent to $\frac{2^{0}2^{3}}{sqrt{2}}$?\na. 0\nb. $sqrt5{2^{2}}$\nc. $sqrt{2^{5}}$\nd. $sqrt3{2^{2}}$\ne. $sqrt{2^{3}}$

Answer

Answer:

C. $\sqrt{2^{5}}$

Explanation:

Step1: Simplify the numerator

$2^{0}\times2^{3}=1\times2^{3}=2^{3}$

Step2: Rewrite the denominator

$\sqrt{2}=2^{\frac{1}{2}}$

Step3: Use the division - rule of exponents

$\frac{2^{3}}{2^{\frac{1}{2}}}=2^{3-\frac{1}{2}}$

Step4: Calculate the exponent

$3-\frac{1}{2}=\frac{6 - 1}{2}=\frac{5}{2}$

Step5: Rewrite the result

$2^{\frac{5}{2}}=\sqrt{2^{5}}$