Chapter 2

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ 4 y^{4} \cdot 5 y^{6} $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ \left(9 x y^{3}\right)^{0} $$

For the following problems, expand the quantities so that no exponents appear. $$ 10 a^{3} b^{2}(3 c)^{2} $$

Use the commutative property of addition and multiplication to write expressions for an equal number for the following problems. You need not perform any calculations. $$\square \cdot[\mathrm{U}+25 \mathrm{CB}]$$

For the following problems, what numbers can replace \(x\) so that the following statements are true? \(-1 \leq x \leq 5 \quad x\) an int eger

For the following problems, rewrite each phrase using algebraic notation. Ten minus three

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ 2 a^{3} b^{2} \cdot 3 a b $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ \left(\frac{1}{2} f^{2} r^{6} s^{5}\right)^{4} $$

For the following problems, expand the quantities so that no exponents appear. $$ (a+10)^{2}\left(a^{2}+10\right)^{2} $$

Use the commutative property of addition and multiplication to write expressions for an equal number for the following problems. You need not perform any calculations.

For the following problems, what numbers can replace \(x\) so that the following statements are true? \(-7

For the following problems, rewrite each phrase using algebraic notation. \(x\) plus sixteen

For the following problems, write the appropriate relation symbol \((=,<,>)\). $$ -8 \quad-5 $$

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ 12 x y^{3} z^{2} \cdot 4 x^{2} y^{2} z \cdot 3 x $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ \left(\frac{1}{8} c^{10} d^{8} e^{4} f^{9}\right)^{2} $$

For the following problems, expand the quantities so that no exponents appear. $$ \left(x^{2}-y^{2}\right)\left(x^{2}+y^{2}\right) $$

Simplify using the commutative property of multiplication for the following problems. You need not use the distributive property. $$9 x 2 y$$

For the following problems, what numbers can replace \(x\) so that the following statements are true? \(-3 \leq x \leq 2, \quad x\) a natural number

For the following problems, rewrite each phrase using algebraic notation. 51 divided by \(a\)

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ (3 a b)\left(2 a^{2} b\right) $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ \left(\frac{3}{5} a^{3} b^{5} c^{10}\right)^{3} $$

For the following problems, select a number (or numbers) to show that \((5 x)^{2}\) is not generally equal to \(5 x^{2}\).

For the following problems, rewrite each phrase using algebraic notation. 81 times \(x\)

Is there a smallest two digit integer? If so, what is it?

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ \left(4 x^{2}\right)\left(8 x y^{3}\right) $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ (x y)^{4}\left(x^{2} y^{4}\right) $$

For the following problems, select a number (or numbers) to show that \((7 x)^{2}\) is not generally equal to \(7 x^{2}\).

For the following problems, what numbers can replace \(x\) so that the following statements are true? \(-5 \leq x<5, \quad x\) a whole number

For the following problems, rewrite each phrase using algebraic notation. 3 times \((x+y)\)

Is there a smallest two digit real number? If so, what is it?

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ (2 x y)(3 y)\left(4 x^{2} y^{5}\right) $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ \left(2 a^{2}\right)^{4}\left(3 a^{5}\right)^{2} $$

For the following problems, select a number (or numbers) to show that \((a+b)^{2}\) is not generally equal to \(a^{2}+b^{2}\).

Simplify using the commutative property of multiplication for the following problems. You need not use the distributive property. $$5 x 10 y 5 z$$

The temperature in the desert today was ninety-five degrees. Represent this temperature by a rational number.

For the following problems, rewrite each phrase using algebraic notation. \((x+b)\) times \((x+7)\)

For the following problems, what integers can replace \(x\) so that the statements are true? $$ 4 \leq x \leq 7 $$

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ \left(\frac{1}{4} a^{2} b^{4}\right) \quad\left(\frac{1}{2} b^{4}\right) $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ \left(a^{2} b^{3}\right)^{3}\left(a^{3} b^{3}\right)^{4} $$

For the following problems, select a number (or numbers) to show that For what real number is \((6 a)^{2}\) equal to \(6 a^{2} ?\)

The temperature today in Colorado Springs was eight degrees below zero. Represent this temperat ure with a real number.

For the following problems, rewrite each phrase using algebraic notation. 3 times \(x\) times \(y\)

For the following problems, what integers can replace \(x\) so that the statements are true? $$ -3 \leq x<1 $$

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ \left(\frac{3}{8}\right)\left(\frac{16}{21} x^{2} y^{3}\right)\left(x^{3} y^{2}\right) $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ \left(h^{3} k^{5}\right)^{2}\left(h^{2} k^{4}\right)^{3} $$

Is every integer a rational number?

For the following problems, rewrite each phrase using algebraic notation. \(x\) divided by \((7\) times \(b)\)

For the following problems, what integers can replace \(x\) so that the statements are true? $$ -3

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ \frac{8^{5}}{8^{3}} $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ \left(x^{4} y^{3} z\right)^{4}\left(x^{5} y z^{2}\right)^{2} $$