Question

Can someone help me with these questions

Answer 1

Answer:

Step-by-step explanation:

When you take the n-th root of a number, you can rewrite the expression by taking it to the 1/n-th power. For example:

$\sqrt[n]{x} =x^\frac{1}{n}$

For the first expression, we can use this proprtery to get:

$\sqrt[5]{a^x} =(a^x)^\frac{1}{5}$

Using exponent rules, you can combine the exponents by simply multiplying them to get:

$a^\frac{x}{5}$

Moving on to the second expression. It is now the square root, or equivalently a 1/2 power. If we break up the terms under the radical into powers of 2, we can cancel a lot of the terms:

$\frac{\sqrt{81a^3b^1^0} }{\sqrt{3}a } =\frac{\sqrt{81a^2*a*b^1^0} }{\sqrt{3}a }$

The a^2 and b^10 can be taken out of the radical because they have perfect roots:

$\frac{\sqrt{81a^2*a*b^1^0} }{\sqrt{3}a }=ab^5\frac{\sqrt{81a} }{\sqrt{3}a }$

The square root of 81 has a perfect root of 9. We have:

$ab^5\frac{\sqrt{81a} }{\sqrt{3}a }=9ab^5\frac{\sqrt{a} }{\sqrt{3}a }$

You can divide 9 and the square root of 3 by breaking up 9 into a product:

$\frac{(3*3)ab^5}{\sqrt{3} } \frac{\sqrt{a} }{a }=3\sqrt{3} ab^5\frac{\sqrt{a} }{a }$

Simply by cancelling the 'a' terms to get:

$3\sqrt{3} ab^5\frac{\sqrt{a} }{a }={3\sqrt{3}}\sqrt{a}b^5=3b^5\sqrt{3a}$