Exam 6: Exponents and Polynomials

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( - 2 a ^ { 8 } b ^ { 5 } \right) ^ { 2 }$

Divide the monomials. $\frac { - 12 z ^ { 12 } q ^ { 10 } c ^ { 7 } } { 6 z ^ { 2 } q ^ { 5 } c ^ { 2 } }$

Use one of the appropriate patterns $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$ $( a - b ) ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 }$ $( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }$ to find the following product. $- 3 x ( 4 - 9 x ) ( 4 + 9 x )$

Use one of the appropriate patterns $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$ ; $( a - b ) ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 }$ ; $( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }$ to find the following product. $( x + 2 ) ^ { 2 }$

Perform the indicated operations. $( 10 x + 6 ) - ( 5 x - 2 ) + ( 4 x + 4 )$

Perform the division of the polynomials by monomials. $\frac { - 30 x ^ { 14 } - 15 x ^ { 13 } + 65 x ^ { 17 } } { 5 x ^ { 2 } }$

Perform the indicated operations and simplify. $( 4 a ) ^ { 2 } \left( 4 a ^ { 2 } \right)$

Find the indicated product by applying the distributive property and combining similar terms. $( x + 9 ) \left( x ^ { 2 } - 5 x - 2 \right)$

Add the polynomials. $7 x + 12,9 x ^ { 4 } + 4 x + 12 \text { and } 10 x ^ { 4 } - 6 x + 15$

Find the product by using the shortcut pattern for multiplying binomials. $( 2 a + 9 ) ( a + 3 )$

Perform the division. $\left( y ^ { 3 } + 27 \right) \div ( y + 3 )$

Perform the division of the polynomials by monomials. $\frac { 6 y c - 48 y ^ { 14 } c ^ { 12 } + 18 y ^ { 19 } c ^ { 18 } } { - 6 y c }$

Use one of the appropriate patterns $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$ ; $( a - b ) ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 }$ ; $( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }$ to find the following product. $- 2 x ( 6 - 9 x ) ( 6 + 9 x )$

Perform the division and find the remainder. $\left( n ^ { 3 } - 4 n ^ { 2 } - 17 n + 2 \right) \div \left( n ^ { 2 } + 3 n \right)$ Remainder: __________

Perform the division and find the quotient. Do not enter the remainder. $\frac { 6 y ^ { 3 } + 34 y ^ { 2 } - 10 y + 10 } { y + 6 }$

Write the following number in standard decimal form. $( 4.34 ) \left( 10 ^ { - 2 } \right)$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 2 v ^ { - 7 } \right) \left( 3 v ^ { 11 } \right)$

Perform the indicated operations. $4 z - \{ 8 z - [ 8 z - ( 9 z - 10 ) ] \}$

Evaluate the following numerical expression. $2 ^ { - 3 }$ Express your answer as an integer or a fraction in lowest terms.

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( \frac { u ^ { - 8 } } { v ^ { - 7 } } \right) ^ { - 1 }$