Dividing with like bases

Dividing with like bases

Dividing with like bases

 $\frac{x^5}{x^3}$  

• if we expand the top it would look like this:  $x\cdot x\cdot x\cdot x\cdot x$  

• if we expand the bottom, it would look like this:  $x\cdot x\cdot x$  

• every "pair" of x's cancel leaving  $x^2$  

But what if that fraction were flipped over?

 $\frac{x^3}{x^5}$  

• since there are more on the bottom, the answer this time would look like this: $\frac{1}{x^2}$  

The real rule is to subtract the exponents.

• Or you can ask

• Which part of the fraction has the larger exponent?

Multiple Choice

 $\frac{d^{15}}{d^8}$  

•  $d^{23}$  

•  $2d^7$  

•  $d^{\frac{15}{8}}$  

•  $d^7$  

Multiple Choice

• y²⁰
• y³
• y²⁶
• 3y

Multiple Choice

Simplify the expression.

• y¹⁵

• y⁵⁰

• y²

• y⁵

Multiple Choice

Simplify and write with positive exponents only.

 $\frac{x^{10}}{x^2}$  

•  $x^{18}$  

•  $x^8$  

•  $x^{20}$  

•  $x^{12}$  

Multiple Choice

Evaluate this expression using the quotient rule.

• 9⁵
• 9⁹
• 1⁵
• 9^-5

Multiple Choice

simplify

 $\frac{x^2}{x^9}$  

•  $x^7$  

•  $\frac{1}{x^7}$  

•  $x^{18}$  

•  $x^{11}$  

Even when different letters are used

 $\frac{x^4y^2}{x^3y^5}$  

• simplify x's and y's  seperatly

•  $\frac{x}{y^3}$  

Multiple Choice

 $\frac{x^{10}y^5}{x^3y^8}$  Hint: divide coefficients

•  $\frac{x^7}{y^3}$  

•  $\frac{x^{13}}{y^{13}}$  

•  $x^7$  

•  $x^{15}y^{11}$  

Multiple Choice

Evaluate the expression using the quotient of powers rule.

• a⁸b¹³

• a²b⁷

• a¹⁵b³⁰

• a⁸b⁷