Chapter 2

For the following problems, write the expressions using exponential notation. \(x\) to the fifth.

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. $$ x^{n} x^{r} $$

Find the value of \(\frac{(5-3)^{2}+(5+4)^{3}+2}{4^{2}-2 \cdot 5-1}\)

For the following problems, write the expressions using exponential notation. \((y+2)\) cubed.

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. $$ a^{x} b^{y} c^{5 z} $$

Assuming the bases are not zero, find the value of \(\left(4 a^{2} b^{3}\right)\left(5 a b^{4}\right)\).

For the following problems, write the expressions using exponential notation. \((a+2 b)\) squared minus \((a+3 b)\) to the fourth.

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. $$ x^{n} \cdot x^{n+3} $$

Assuming the bases are not zero, find the value of \(\frac{36 x^{10} y^{8} z^{3} w^{0}}{9 x^{5} y^{2} z}\).

For the following problems, write the expressions using exponential notation. \(x\) cubed plus 2 times \((y-x)\) to the seventh.

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. $$ \frac{x^{n+3}}{x^{n}} $$

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. $$ \frac{x^{n+2} x^{3}}{x^{4} x^{n}} $$

For the following problems, write the expressions using exponential notation. \(2 \cdot 2 \cdot 2 \cdot 2\)

For the following problems, write the expressions using exponential notation. $$ (-8)(-8)(-8)(-8) x x x y y y y y $$

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.

For the following problems, write the expressions using exponential notation. $$ (x-9)(x-9)+(3 x+1)(3 x+1)(3 x+1) $$

For the following problems, write the expressions using exponential notation. $$ (x-9)(x-9)+(3 x+1)(3 x+1)(3 x+1) $$

For the following problems, expand the terms so that no exponents appear. $$ x^{3} $$

What natural numbers can replace \(x\) so that the statement \(-5

For the following problems, expand the terms so that no exponents appear. $$ 3 x^{3} $$

Use the distributive property to exp and \(4 x(2 a+3 b)\).

For the following problems, expand the terms so that no exponents appear. $$ 7^{3} x^{2} $$

Express \(x x x y y y y(a+b)(a+b)\) using exponents.

For the following problems, expand the terms so that no exponents appear. $$ (4 b)^{2} $$

Find the value of \(4^{2}+3^{2} \cdot 2^{3}-10 \cdot 8\).

For the following problems, expand the terms so that no exponents appear. $$ \left(6 a^{2}\right)^{3}(5 c-4)^{2} $$

Find the value of \(\frac{4^{2}+(3+2)^{2}-1}{2^{3} \cdot 5}+\frac{2^{4}\left(3^{2}-2^{3}\right)}{4^{2}}\).

For the following problems, expand the terms so that no exponents appear. $$ \left(x^{3}+7\right)^{2}\left(y^{2}-3\right)^{3}(z+10) $$

Choose values for \(a\) and \(b\) to show that a. \((a+b)^{2}\) is not always equal to \(a^{2}+b^{2}\). b. \((a+b)^{2}\) may be equal to \(a^{2}+b^{2}\).

Choose value for \(x\) to show that a. \((4 x)^{2}\) is not always equal to \(4 x^{2}\). b. \((4 x)^{2}\) may be equal to \(4 x^{2}\).

Simplify the following problems. $$ 4^{2}+8 $$

Simplify the following problems. $$ 6^{3}+5(30) $$

Simplify the following problems. $$ 1^{8}+0^{10}+3^{2}\left(4^{2}+2^{3}\right) $$

Simplify the following problems. $$ 12^{2}+0.3(11)^{2} $$

Simplify the following problems. $$ \frac{3^{4}+1}{2^{2}+4^{2}+3^{2}} $$

Simplify the following problems. $$ \frac{6^{2}+3^{2}}{2^{2}+1}+\frac{(1+4)^{2}-2^{3}-1^{4}}{2^{5}-4^{2}} $$

Simplify the following problems. $$ a^{4} a^{3} $$

Simplify the following problems. $$ 2 b^{5} 2 b^{3} $$

Simplify the following problems. $$ 4 a^{3} b^{2} c^{8} \cdot 3 a b^{2} c^{0} $$

Simplify the following problems. $$ \left(6 x^{4} y^{10}\right)\left(x y^{3}\right) $$

Simplify the following problems. $$ \left(3 x y z^{2}\right)\left(2 x^{2} y^{3}\right)\left(4 x^{2} y^{2} z^{4}\right) $$

Simplify the following problems. $$ (3 a)^{4} $$

Simplify the following problems. $$ (10 x y)^{2} $$

Simplify the following problems. $$ \left(x^{2} y^{4}\right)^{6} $$

Simplify the following problems. $$ \left(a^{4} b^{7} c^{7} z^{12}\right)^{9} $$

Simplify the following problems. $$ \left(\frac{3}{4} x^{8} y^{6} z^{0} a^{10} b^{15}\right)^{2} $$

Simplify the following problems. $$ \frac{x^{8}}{x^{5}} $$

Simplify the following problems. $$ \frac{14 a^{4} b^{6} c^{7}}{2 a b^{3} c^{2}} $$

Simplify the following problems. $$ \frac{11 x^{4}}{11 x^{4}} $$

Simplify the following problems. $$ x^{4} \cdot \frac{x^{10}}{x^{3}} $$