Math Help - Exponent laws,rationalization and interval notation

1. Exponent laws,rationalization and interval notation

The expression
equals
where r, the exponent of h, is: ?
and t, the exponent of s, is: ?
and k, the leading coefficient is: 2

If you rationalize the denominator of
then you will get
where , , and are all positive integers (with no common factors).

7
4
?

Solve the following inequality. Write the answer in interval notation.
Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter as infinity and as -infinity .

4< 3x+1 <6

2. Originally Posted by wannous
The expression
equals
where r, the exponent of h, is: ?
and t, the exponent of s, is: ?
and k, the leading coefficient is: 2

If you rationalize the denominator of
then you will get
where , , and are all positive integers (with no common factors).

7
4
?

Solve the following inequality. Write the answer in interval notation.
Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter as infinity and as -infinity .

4< 3x+1 <6
$\frac{\sqrt[4]{16h^{-9}s^{-5}}}{\sqrt[4]{h^{-8}s^3}} = \sqrt[4]{\frac{16h^{-9}s^{-5}}{h^{-8}s^3}} = \sqrt[4]{16h^{-1}s^{-8}} = (16h^{-1}s^{-8})^{\frac{1}{4}} =$ ?

$\frac{1}{7\sqrt{5}-4\sqrt{3}} \cdot \frac{7\sqrt{5}+4\sqrt{3}}{7\sqrt{5}+4\sqrt{3}}$ = ?

$4< 3x+1 < 6$

subtract 1 from all terms ...

$3 < 3x < 5$

last step is to divide all terms by 3 ...

3. thank you very much