Exam 5: Exponents, Polynomials, and Polynomial Functions

Simplify: $\frac { \left( 6 ^ { 5 m } \right) ^ { - 2 } \cdot 6 ^ { 3 m } } { \left( 6 ^ { 2 m } \right) ^ { - 7 } \cdot 6 ^ { 6 m } \cdot 6 ^ { - 2 m } }$ Assume there are no divisions by zero.

Factor the expression completely. If the expression is prime, so indicate. $- 3 x ^ { 3 } + 81$

Evaluate: $( - 7 ) ^ { 0 }$

Solve the equation. $b ( 5 b - 6 ) = 8$

Simplify the expression. Write the answer using positive exponents. $\frac { 1 } { 8 ^ { - 2 } }$

Write the equation in standard form. $9 - 10 x = - x ^ { 2 }$

Multiply. $( 3 y + 2 ) \left( 2 y ^ { 2 } + 3 y + 2 \right)$

Write the number in scientific notation. $0.0314 \times 10 ^ { - 2 }$

Factor the expression completely. $x ^ { 2 } - y ^ { 2 } - 2 y - 1$ If the expression is prime, so indicate.

Factor: $\log _ { 3 } x + \log _ { 3 } ( x - 8 ) = 2$ Assume that n is a natural number.

Add. $\left( 3 x ^ { 2 } + 2 x + 2 \right) + \left( - 2 x ^ { 2 } - 6 x + 5 \right)$

Simplify the expression. $\left( x ^ { 3 } \right) ^ { 9 }$

The cost for a guitar maker to handcraft x guitars is given by the function $C ( x )$ . The revenue taken in with the sales of x guitars is given by the function $R ( x )$ . Find the number of guitars that must be sold so that the cost equals the revenue. $C ( x ) = \frac { 1 } { 8 } x ^ { 2 } + x + 16$ , $R ( x ) = \frac { 1 } { 4 } x ^ { 2 }$

Subtract $2 x ^ { 2 } - 4 x + 2$ from the sum of $8 x ^ { 2 } + 5 x - 2 \text { and } - 2 x ^ { 2 } + 7 x - 4$ .

If $f ( x ) = x ^ { 2 } - 6 x - 7 \text {, find } f ( a + h ) - f ( a )$

Factor, if possible. $20 x ^ { 2 } y - 16 x ^ { 2 } y ^ { 2 }$

Since $x ^ { 2 } + 10 x + 25$ is the square of $x + 5$ , it is called a __________-square trinomial.

Multiply. $( 4 t - 3 ) ( 6 t + 7 )$

Factor the expression completely. $16 x ^ { 2 } y ^ { 3 } + 8 x y ^ { 3 } + y ^ { 3 }$ If the expression is prime, so indicate.

Solve the equation. $y ^ { 2 } - 25 = 0$