Chapter 2

For the following problems, simplify the expressions. $$ 12+7(4+3) $$

Find each product. $$ x^{2} \cdot x^{5} $$

Simplify each expression using the power rule for powers. $$ \left(x^{5}\right)^{4} $$

Write each of the following using exponents. \(a \cdot a \cdot a \cdot a\)

Fill in the \((\quad)\) with the proper number or letter so as to make the statement true. Use the commutative properties. $$6+5=(\quad)+6$$

Is every natural number a whole number?

Represent the product of 29 and \(x\) five different ways. If we let \(a\) and \(b\) represent two numbers, then \(a\) and \(b\) are related in exactly one of three ways:

For the following problems, simplify the expressions. $$ 9(4-2)+6(8+2)-3(1+4) $$

Find each product. $$ x^{9} \cdot x^{4} $$

Simplify each expression using the power rule for powers. $$ \left(y^{7}\right)^{7} $$

Write each of the following using exponents. \((3 b)(3 b)(5 c)(5 c)(5 c)(5 c)\)

Fill in the \((\quad)\) with the proper number or letter so as to make the statement true. Use the commutative properties. $$m+12=12+(\quad)$$

Is every whole number an integer?

Use the grouping symbols to help perform the following operations. $$3(1+8)$$

For the following problems, simplify the expressions. $$ 6[1+8(7+2)] $$

Find each product. $$ y^{6} \cdot y^{4} $$

Make use of either or both the power rule for products and the power rule for powers to simplify each expression. $$ (a x)^{4} $$

Write each of the following using exponents. \(2 \cdot 2 \cdot 7 \cdot 7 \cdot 7 \cdot(a-4)(a-4)\)

Fill in the \((\quad)\) with the proper number or letter so as to make the statement true. Use the commutative properties. $$9 \cdot 7=(\quad) \cdot 9$$

Is every integer a rational number?

Use the grouping symbols to help perform the following operations. $$4[2(11-5)]$$

For the following problems, simplify the expressions. $$ 26 \div 2-10 $$

Find each product. $$ c^{12} \cdot c^{8} $$

Make use of either or both the power rule for products and the power rule for powers to simplify each expression. $$ (3 b x y)^{2} $$

Write each of the following using exponents. \(8 x x x y z z z z z\)

Fill in the \((\quad)\) with the proper number or letter so as to make the statement true. Use the commutative properties. \(6 a=a(\quad)\)

Is every rational number a real number?

Use the grouping symbols to help perform the following operations. $$6\\{2[2(10-9)]\\}$$

For the following problems, simplify the expressions. $$ \frac{(4+17+1)+4}{14-1} $$

Find each product. $$ (x+2)^{3} \cdot(x+2)^{5} $$

Make use of either or both the power rule for products and the power rule for powers to simplify each expression. $$ [4 t(s-5)]^{3} $$

Write each of the following without exponents. $$ 4 a^{3} $$

Fill in the \((\quad)\) with the proper number or letter so as to make the statement true. Use the commutative properties. $$4(k-5)=(\quad) 4$$

Is every integer a natural number?

Use the grouping symbols to help perform the following operations. $$\frac{1+19}{2+3}$$

Perform each multiplication in one step. $$ 3 x^{5} \cdot 2 x^{2} $$

For the following problems, simplify the expressions. $$ 51 \div 3 \div 7 $$

Write each of the following without exponents. $$ (4 a)^{3} $$

Is there an integer that is a natural number?

Use the order of operations to find each value. $$25+8(3)$$

For the following problems, simplify the expressions. $$ (4+5)(4+6)-(4+7) $$

Perform each multiplication in one step. $$ 6 y^{3} \cdot 3 y^{4} $$

Make use of either or both the power rule for products and the power rule for powers to simplify each expression. $$ \left(1 a^{5} b^{8} c^{3} d\right)^{6} $$

Select a number to show that \((5 x)^{2}\) is not always equal to \(5 x^{2}\).

Fill in the ( ) to make each statement true. Use the associative properties. $$(9+2)+5=9+(\quad)$$

Are all positive numbers greater than 0 ?

Use the order of operations to find each value. $$2+3(18-5 \cdot 2)$$

For the following problems, simplify the expressions. $$ 8(2 \cdot 12 \div 13)+2 \cdot 5 \cdot 11-[1+4(1+2)] $$

Perform each multiplication in one step. $$ 4 a^{3} b^{2} \cdot 9 a^{2} b $$

Make use of either or both the power rule for products and the power rule for powers to simplify each expression.] $$ [(a+8)(a+5)]^{4} $$