5.3 Homework: extending the idea of exponents

$5^0$

$5^{-2}$

$=-2^{-2}$

$=-2^{-3}$

$=6^{-3}$

$x^0=$

$(x-a)()=$

Let’s look at the problem $6^{0}6^x$ two different ways.

• a What is $6^0$ ? Based on that, what is $6^{0}6^x$ ?
• b What do our rules of exponents tell us about $6^{0}6^x$ ?

Let’s look at the problem $\frac{6^0}{6^x}$ two different ways.

• a What is $6^0$ ? Based on that, what is $\frac{6^0}{6^x}$ ?
• b What do our rules of exponents tell us about $\frac{6^0}{6^x}$ ?

Let’s look at the problem $6^{-4}6^3$ two different ways.

• a What does $6^{-4}$ mean? Based on that, what is $6^{-4}6^3$ ?
• b What do our rules of exponents tell us about $6^{-4}6^3$ ?

What would you square if you wanted to get $x^{36}$ ?

$\frac{1}{x^{-5}}$

$\frac{{\mathrm{8x}}^3{y}^7}{\text{12}{x}^{-3}{y}^4}$

Solve for $x$ : $3^{(x+2)}=3^{(8-x)}$ . ( Hint : If the bases are the same, the exponents must be the same!)

Solve for $x$ : $2^{\mathrm{4x}-3}=8^{x-2}$ .

Solve for $x$ : $5^{({\mathrm{3x}}^2+\text{13}x+\text{10})}=25^{(x+2)}$ . (*No more hints this time, you’re on your own.)

Solve for $x$ : $7^{x}7^{(x+2)}=1$

Solve for $x$ : $7^x^{(x+2)}=1$