which expression is equivalent to $left\frac{4^{\frac{5}{4}}cdot4^{\frac{1}{4}}}{4^{\frac{1}{2}}}\right^{\fra…

which expression is equivalent to $left\frac{4^{\frac{5}{4}}cdot4^{\frac{1}{4}}}{4^{\frac{1}{2}}}\right^{\frac{1}{2}}$?\n$sqrt16{4^{5}}$\n$sqrt{2^{5}}$\n$2$\n$4$

which expression is equivalent to $left\frac{4^{\frac{5}{4}}cdot4^{\frac{1}{4}}}{4^{\frac{1}{2}}}\right^{\frac{1}{2}}$?\n$sqrt16{4^{5}}$\n$sqrt{2^{5}}$\n$2$\n$4$

Answer

Answer:

C. 2

Explanation:

Step1: Use exponent - product rule

When multiplying numbers with the same base (a^m\cdot a^n=a^{m + n}), so (4^{\frac{5}{4}}\cdot4^{\frac{1}{4}}=4^{\frac{5 + 1}{4}}=4^{\frac{6}{4}}).

Step2: Simplify the exponent

(4^{\frac{6}{4}}=4^{\frac{3}{2}}). Then the original expression becomes (\left(\frac{4^{\frac{3}{2}}}{4^{\frac{1}{2}}}\right)^{\frac{1}{2}}).

Step3: Use exponent - quotient rule

When dividing numbers with the same base (\frac{a^m}{a^n}=a^{m - n}), so (\frac{4^{\frac{3}{2}}}{4^{\frac{1}{2}}}=4^{\frac{3}{2}-\frac{1}{2}}=4^1).

Step4: Calculate the final result

The expression is now ((4^1)^{\frac{1}{2}}). Using the power - of - a - power rule ((a^m)^n=a^{mn}), we have (4^{\frac{1}{2}}=\sqrt{4}=2).