Question

MEDAL AND BEST RESPONSE! HELP!

What is the exact value of 5 times q cubed all over the square root of q to the eleventh power.? Simplify if possible.

5 the square root of q all over q to the seventh power.

5 the square root of q all over q to the eighth power.

5 the square root of q all over q squared.

5 the square root of q all over q cubed.

Answer 1

\[\frac{ 5q^3 }{ \sqrt{q ^{11}} }\]We can take the denominator and expand it..\[\frac{ 5q^3 }{ \sqrt{q ^{10}q} }\]Then we can take the root of the first part and simplify it to the outside of the radical...\[\frac{ 5q^3 }{ q^5\sqrt{q} }\]Finally, we can apply the exponent law concerning division and subtract the two q's exponents to get..\[\frac{ 5 }{ q^2\sqrt{q} }\]Actually, there's one more step before this is fully simplified. We have to move the radical to the numerator so we'll multiply..\[\frac{ 5 }{ q^2\sqrt{q} }*\frac{ \sqrt{q} }{ \sqrt{q} }\]
(We're allowed to do this since we're really multiplying by one in disguise.) This simplifies to..\[\frac{ 5\sqrt{q} }{ q^3 }\](The q to the third power was created as a product of the two root q's and the q squared.)

Hope this helped!

Answer 2

thank you!