Exam 10: Rational Exponents, Radicals, and Complex Numbers

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { 5 } { \sqrt [ 3 ] { 36 x ^ { 2 } } }$

Factor the given factor from the expression. - $x ^ { - 4 / 5 } ; x ^ { 6 / 5 } + x ^ { - 4 / 5 }$

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - $- \sqrt [ 4 ] { x ^ { 8 } }$

Perform the indicated operation. Write the result in the form a + bi. - $\frac { 3 } { 5 i }$

Write with positive exponents. Simplify if possible. - $x ^ { - 3 / 7 }$

Use the quotient rule to divide and simplify. - $\frac { \sqrt { 96 } } { \sqrt { 4 } }$

Perform the indicated operations. Assume that all variables represent positive numbers. - $( \sqrt { x } - 18 ) ^ { 2 }$

Find the power of i. - $\mathrm { i } ^{15}$

Solve. - $x - \sqrt { 26 x + 39 } = - 8$

Solve. - $\sqrt { 8 x - 7 } = \sqrt { x + 11 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( \sqrt { x - 3 } + 4 ) ^ { 2 }$

Solve. -Find the perimeter of the trapezoid. Simplify.

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { 7 - \sqrt { 6 } } { 7 + \sqrt { 6 } }$

Add or subtract. Assume all variables represent positive real numbers. - $\sqrt { 3 } - 6 \sqrt { 75 } + 3 \sqrt { 27 }$

Use the Pythagorean theorem to find the unknown side of the right triangle. -

Use radical notation to write the expression. Simplify if possible. - $\left( 81 x ^ { 6 } \right) ^ { 1 / 2 }$

Perform the indicated operation. Write the result in the form a + bi. -(9 - 72i)(8 - i)

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( 3 \sqrt { x } + 5 ) ( \sqrt { 3 x } - 5 )$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $\sqrt { 7 } ( \sqrt { 28 } + \sqrt { 14 } )$

Identify the domain and then graph the function. - $f(x)=\sqrt[3]{x}-3$