Exam 1: A Review of Basic Algebra

Simplify the expression. $\frac { x ^ { 7 } x ^ { 4 } } { x ^ { 4 } x }$ Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

Simplify the expression. $- 25 ^ { 4 / 2 }$

Simplify the expression. $\frac { a ^ { 1 / 5 } a ^ { 4 / 5 } } { a ^ { 2 / 5 } }$ Write all answers without using negative exponents. Assume that all variables represent positive numbers.

Perform the operations and simplify. $\left( 7 x ^ { 3 } - 5 x ^ { 2 } \right) + \left( 7 x ^ { 3 } - 5 x \right)$

Simplify each complex fraction. $\frac { x + 2 - \frac { 63 } { x } } { x + 16 + \frac { 63 } { x } }$ Assume that no denominators are 0 .

Factor the expression completely. $( 2 x - 5 y ) ^ { 3 } + 125$

Factor the expression completely. $z ^ { 2 } + 8 z + 16 - 196 y ^ { 2 }$

Factor the expression completely. $3 x ^ { 3 } + 3 x ^ { 2 } - 13 x - 13$

Simplify the expression. $\frac { a ^ { 3 / 7 } a ^ { 2 / 7 } } { a ^ { 1 / 7 } }$ Write all answers without using negative exponents.Assume that all variables represent positive numbers.

Simplify the expression. $\left( x ^ { 5 } \right) ^ { 4 } \left( x ^ { 3 } \right) ^ { 3 }$

How many natural numbers are there between -12.5 and 6.5 on the number line?

Simplify each complex fraction. $\frac { x + 1 - \frac { 6 } { x } } { x + 5 + \frac { 6 } { x } }$ Assume that no denominators are 0 .

Perform division and write the answer without using negative exponents. $\frac { - 190 x ^ { 6 } y ^ { 4 } z ^ { 9 } } { 19 x ^ { 9 } y ^ { 6 } z ^ { 0 } }$

Simplify the radical expression. $\sqrt [ 4 ] { 4 }$

Perform the operations and simplify. $\frac { 2 a } { 13 } \cdot \frac { 3 } { 5 b }$ Assume that no denominators are 0.

Simplify the fraction. $\frac { 7 x - 49 } { x ^ { 2 } - 49 }$ Assume that the denominator is not 0 .

Simplify the expression. $\left( - \frac { 3,125 x ^ { 10 } } { 32 y ^ { 5 } } \right) ^ { 1 / 5 }$

Perform the operations and simplify. $\frac { 23 a } { 2 } \cdot \frac { 11 } { 2 b }$ Assume that no denominators are 0 .

Simplify the expression. $\left( \frac { 7 x ^ { - 5 } y ^ { 3 } z ^ { - 4 } } { 28 x ^ { 6 } y ^ { 11 } z ^ { - 9 } } \right) ^ { 3 }$ Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Perform the operation and simplify. $- 3 a ^ { 2 } ( a + 1 ) + 9 a \left( a ^ { 2 } - 6 \right) - a ^ { 2 } ( a + 6 )$