Exam 1: Review of Basic Concepts

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 1 } { 5 } \left( 10 y + \frac { 10 } { 3 } x - 20 \right)$

Factor the trinomial, if possible. - $x ^ { 2 } - x - 56$

Evaluate the expression. - $\left( - \frac { 64 } { 125 } \right) ^ { - 4 / 3 }$

Determine the degree of the polynomial. - $4 a ^ { 2 } + 16 a ^ { 5 } - 5 a$

Factor, using the given factor. Assume all variables represent positive real numbers. - $12 y ^ { 4 } ( 2 y + 1 ) ^ { - 2 / 5 } + 16 y ^ { 3 } ( 2 y + 1 ) ^ { 3 / 5 } - 32 y ^ { 2 } ( 2 y + 1 ) ^ { 8 / 5 } ; \quad 4 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 200 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }$

Factor the trinomial, if possible. - $- 24 x ^ { 2 } - 20 x + 24$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -In an economics study, three quantities m, p, and q have been found to be related by the equation $m = p ^ { 1 / 2 } \cdot q ^ { 1 / 2 } . \text { Find } m \text {, if } p = 4 \text { and } q = 16$

Factor the trinomial, if possible. - $15 x ^ { 2 } + 22 x + 8$

Factor by any method. - $25 z ^ { 4 } + 5 z ^ { 2 } - 12$

Factor the trinomial, if possible. - $( x + 4 y ) ^ { 2 } + 6 ( x + 4 y ) + 9$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 5 ] { \mathrm { x } ^ { 18 } \mathrm { y } ^ { 9 } \mathrm { z } ^ { 14 } }$

Find the sum or difference. - $( 6 y - 5 ) \left( 36 y ^ { 2 } + 30 y + 25 \right)$

Find the sum or difference. - $[ ( 8 x + 5 ) + 6 y ] ^ { 2 }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. -A simple exercise machine can be constructed by mounting a stiff spring securely to a wall and attaching a "T" handle to the free end of the spring. The arms can be exercised simply by pulling the "T" handle towards the Torso. For a particular spring, the stretch distance is related to the work exerted by the equation x $x = \sqrt { \frac { 2 W } { 85000 } }$ where W is the work exerted in joules and x is the stretch distance in cm. How far will you stretch the spring if You exert 669 joules of work? Round your answer to three decimal places.

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { \frac { 3 } { 5 } }$

Find the sum or difference. - $( 4 a - 7 ) ^ { 2 }$

Find the sum or difference. - $( 2 x - 2 ) ^ { 4 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $x ^ { 4 } \cdot x ^ { 2 }$

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { x ^ { 2 } - 36 y ^ { - 2 } } { \left( x - 6 y ^ { - 1 } \right) \left( x + 6 y ^ { - 1 } \right) }$