Chapter 7
Algebra 2 and Trigonometry · 288 exercises
Problem 37
Solve each equation and check. \(e^{2 x+2}=e^{x-1}\)
3 step solution
Problem 38
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt{7} $$
2 step solution
Problem 38
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ 2 x^{-2} $$
3 step solution
Problem 38
Solve each equation and check. \(3^{x^{2}+2}=3^{6}\)
4 step solution
Problem 39
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt{6} $$
3 step solution
Problem 39
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ 7 a^{-4} $$
5 step solution
Problem 40
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt[3]{12} $$
3 step solution
Problem 40
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ -5 y^{-8} $$
3 step solution
Problem 41
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt[3]{15} $$
3 step solution
Problem 41
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ (2 x)^{-2} $$
4 step solution
Problem 42
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt[4]{3} $$
3 step solution
Problem 42
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ (3 a)^{-4} $$
5 step solution
Problem 43
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt[5]{2^{3}} $$
4 step solution
Problem 43
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ (4 y)^{-3} $$
4 step solution
Problem 44
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ (\sqrt[5]{9})^{4} $$
5 step solution
Problem 44
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ -(2 x)^{-2} $$
3 step solution
Problem 45
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \frac{1}{(\sqrt{5})^{3}} $$
4 step solution
Problem 45
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ -(3 a)^{-4} $$
4 step solution
Problem 46
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt{25 a} $$
5 step solution
Problem 46
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ (-2 x)^{-2} $$
3 step solution
Problem 47
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt{49 x^{2}} $$
5 step solution
Problem 47
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \frac{1}{x^{-3}} $$
3 step solution
Problem 48
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt{64 a^{3} b^{6}} $$
5 step solution
Problem 48
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \frac{1}{y^{-7}} $$
3 step solution
Problem 49
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \frac{1}{2} \sqrt{18 a^{6} b^{2}} $$
5 step solution
Problem 49
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \frac{3}{a^{-5}} $$
4 step solution
Problem 50
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt{9 a^{-2} b^{6}} $$
5 step solution
Problem 50
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \frac{6}{a^{-4}} $$
3 step solution
Problem 51
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt{\frac{3 a}{4 b}} $$
5 step solution
Problem 51
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \frac{9 x^{2}}{a^{-3}} $$
2 step solution
Problem 52
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt[3]{27 a^{3}} $$
4 step solution
Problem 52
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \frac{(-x)^{-5}}{x^{-3}} $$
7 step solution
Problem 53
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt[4]{64 x^{5}} $$
6 step solution
Problem 53
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \frac{(2 a)^{-1}}{2(a)^{-2}} $$
5 step solution
Problem 54
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \frac{1}{\sqrt[5]{x y z^{5}}} $$
4 step solution
Problem 54
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \frac{4 y^{-3}}{2 y^{-1}} $$
4 step solution
Problem 55
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt{\frac{9 a^{-2}}{4 b^{4}}} $$
4 step solution
Problem 55
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \left(x y^{5} z^{-2}\right)^{-1} $$
2 step solution
Problem 56
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt[10]{\frac{w^{15} x^{20}}{y^{5}}} $$
4 step solution
Problem 56
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \left(a^{5} b^{-5} c^{-4}\right)^{-3} $$
5 step solution
Problem 57
In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt[8]{\sqrt[4]{a} \cdot \sqrt[4]{b^{7}}} $$
5 step solution
Problem 57
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \left(\frac{3 m^{-3}}{2 n^{-2}}\right)^{-3} $$
5 step solution
Problem 58
In \(58-73\) , write each power as a radical expression in simplest form. The variables are positive numbers. $$ 3^{\frac{1}{2}} $$
3 step solution
Problem 58
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \left(\frac{6 a b^{4}}{3 x^{-3} y^{-4}}\right)^{-1} $$
3 step solution
Problem 59
In \(58-73\) , write each power as a radical expression in simplest form. The variables are positive numbers. $$ 5^{\frac{1}{2}} $$
3 step solution
Problem 59
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \frac{x^{5} y^{-4}}{x^{-4} y^{-2}} $$
4 step solution
Problem 60
In \(58-73\) , write each power as a radical expression in simplest form. The variables are positive numbers. $$ 6^{\frac{1}{3}} $$
3 step solution
Problem 60
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \left(3 a b^{-2}\right)\left(3 a^{-1} b^{3}\right) $$
3 step solution
Problem 61
In \(58-73\) , write each power as a radical expression in simplest form. The variables are positive numbers. $$ 9^{\frac{1}{3}} $$
3 step solution
Problem 61
In \(35-63,\) write each expression with only positive exponents and express the answer in simplest form. The variables are not equal to zero. $$ \frac{-64 x^{4} a^{-2}}{2 x^{5} b^{-4}} $$
5 step solution