Simplify 4^sqrt 400/4^sqrt 5. how to?

Question

baru · Answer

can you use the equation button? its hard to interpret what you have typed

daniel.ohearn1 · Answer

If you can take a screenshot of the problem that would help, attach it as a file too..

jiteshmeghwal9 · Answer

$$\LARGE{4^{\sqrt{400}} \over {4^\sqrt{5}}}$$

jiteshmeghwal9 · Answer

$$\LARGE{4^{20-\sqrt{5}}}$$as$$\LARGE{{a^b \over a^c}=a^{b-c}}$$

denonakavro · Answer

$$4^{400}\div4^{5} $$
Just subtract 400-5 = 395
SO the answer will be 4^395

faiqraees · Answer

@denonakavro Please check the question again. The exponent with the second number is $$\sqrt{5}$$ not simply 5

whpalmer4 · Answer

@jiteshmegwhal9 has it correct.  The step left out is reducing $\sqrt{400}$ to $20$

$$\frac{4^{\sqrt{400}}}{4^{\sqrt{5}}}=\frac{4^{20}}{4^{\sqrt{5}}}$$and because$$\frac{b^m}{b^n} = b^{m-n}$$we can then rewrite that as $$4^{20-\sqrt{5}}$$
The approximate value of that is $49539630091.22790143784586$, if you were wondering :-)