Exam 12: Review of Basic Concepts

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

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { 27 x y ^ { 2 } } \cdot \sqrt [ 3 ] { 3 y ^ { 2 } } } { \sqrt [ 3 ] { 243 x y ^ { 4 } } }$

Factor the polynomial by substitution. - $60 z ^ { 8 } - 44 z ^ { 5 } - 48 z ^ { 2 }$

Find the sum or difference. - $\left( 5 x ^ { 4 } - 7 x ^ { 2 } + x \right) - \left( 9 x ^ { 3 } + 6 x ^ { 2 } + 2 x \right) + \left( 5 x ^ { 2 } - x \right)$

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 6,7,8,9,10,11,12,13,14,15,16 \} , \mathrm { M } = \{ 6,8,10,12 \} , \mathrm { N } = \{ 7,9,11,13,15 \}$ , $Q = \{ 6,8,10,12,14,16 \}$ , and $R = \{ 6,7,8,9 \}$ . $\mathrm { N } ^ { \prime }$

Write in radical form. Assume all variables represent positive real numbers. - $\mathrm { x } ^ { 1 / 7 }$

Find the product. - $\left( 2 x ^ { 3 } - x ^ { 2 } + 4 x - 1 \right) ( 2 x + 3 )$

Provide an appropriate response. -The formula used to find the volume of the frustum of a square pyramid is $V = \frac { 1 } { 3 } h \left( a ^ { 2 } + a b + b ^ { 2 } \right)$ , where $b$ is the length of the base, $a$ is the length of the top, and $h$ is the height. Calculate the volume if $a = 263$ feet , $b = 698$ feet , and $h = 192$ feet.

Factor the trinomial, if possible. - $36 x ^ { 2 } + 21 x y + 3 y ^ { 2 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $- \left( \frac { 5 x ^ { 3 } } { y ^ { 2 } } \right) ^ { 0 }$

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true. -{ 9 }______{ 9,10,11,12,13,14 }

Factor by any method. - $50 \times 10 - 32$

Find the product or quotient. - $\frac { k ^ { 2 } + 13 k + 40 } { k ^ { 2 } + 16 k + 64 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } - 3 k - 40 }$

Factor the trinomial, if possible. - $2 x ^ { 2 } - 12 x + 16$

Determine the degree of the polynomial. - $- x - 4 x ^ { 2 } - 4 x ^ { 3 } - 4 x ^ { 5 }$

Tell whether the statement is true or false. - $\{ 7,10,11,13 \} \cap \{ 10,11,14,15 \} = \{ 10,11 \}$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt { 150 } } { 2 } - \frac { 3 \sqrt { 6 } } { 2 } + \frac { \sqrt { 6 } } { \sqrt { 4 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { 4 } { \sqrt [ 3 ] { 5 } } - \frac { 31 } { \sqrt [ 3 ] { 40 } } + \frac { 1 } { \sqrt [ 3 ] { 135 } }$

Write the expression in lowest terms. - $\frac { 8 z + 24 } { 3 z + 9 }$

Evaluate the expression. - $91 - 20 \cdot 3 + 23$