Exam 1: A Review of Basic Algebra

Simplify the expression. $\left( \frac { a ^ { - 5 } } { b ^ { - 3 } } \right) ^ { - 4 }$ Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Calculate the volume of a box that has dimensions of 6,000 by 9,300 by 4,300 millimeters.

Perform the multiplication and simplify. $( x - y ) ( 3 x + 14 y ) ^ { 2 }$

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

Simplify the fraction. $\frac { x y + 6 x + 9 y + 54 } { x ^ { 3 } + 729 }$ Assume that denominator is not 0 .

Rationalize the denominator and simplify. $\frac { 4 } { \sqrt [ 4 ] { 4 } }$

Simplify the expression. $\left( 625 y ^ { 4 } \right) ^ { 1 / 4 }$

Perform the operation and simplify. $- 3 a ^ { 2 } ( a + 1 ) + 6 a \left( a ^ { 2 } - 4 \right) - a ^ { 2 } ( a + 10 )$

Simplify the radical expression. $\sqrt [ 6 ] { 8 }$

Factor the expression completely. $36 z ^ { 2 } + 84 z + 49$

Select the correct representation of the inequality in interval notation. $x \leq 7$

Simplify the expression. $\frac { 1 } { x ^ { - 7 } }$ 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. $\left( 9 y ^ { 2 } \right) ^ { 1 / 2 }$

Rationalize the denominator and simplify. $\frac { 2 } { \sqrt [ 3 ] { 2 } }$

We can often multiply and divide radicals with different indexes.For example: $\sqrt { 3 } \sqrt [ 3 ] { 5 } = \sqrt [ 6 ] { 27 } \sqrt [ 6 ] { 25 } = \sqrt [ 6 ] { ( 27 ) ( 25 ) } = \sqrt [ 6 ] { 675 }$ Use this idea to write the following expression as a single radical.

Perform the operations and simplify. $\left( 5 x ^ { 3 } - 6 x ^ { 2 } \right) + \left( 9 x ^ { 3 } - 3 x \right)$

Express the number -174,000,000 in scientific notation.

Simplify the complex fraction. $\frac { \frac { 4 x ^ { 2 } } { y ^ { 4 } } } { \frac { 8 x ^ { 3 } z ^ { 3 } } { y ^ { 2 } } }$ Assume that the denominators are not 0.

Multiply the expression as you would multiply polynomials. $\left( a ^ { 11 / 2 } + b ^ { 3 / 2 } \right) \left( a ^ { 11 / 2 } - b ^ { 3 / 2 } \right)$

Simplify the expression. $\frac { x ^ { 6 } x ^ { 4 } } { x ^ { 3 } x }$ Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.