Power to Power Same Base

​Same Base Exponents

​What do we do?

Keep the base the same and add the exponents ​

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Now try some examples on the next slides ​

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Multiple Choice

Simplify the expression:
(a⁵)(a⁴)

• a²⁰
• a⁹
• a¹

Multiple Choice

$$x^3\ \cdot\ x^4$$

• $$x^{12}$$  

• $$2x^7$$  

• $$x^7$$  

• $$2x^{12}$$  

Multiple Choice

• y¹⁶
• y³
• 16y
• y⁴⁸

​What if I have a power to a power?

What do I do?

​Multiply the exponents together

Multiple Choice

• a
• b

Multiple Choice

Simplify the expression in exponential form: (5⁴)³

• 5¹
• 5⁷
• 5¹²

Multiple Choice

(3y⁴)²

• 9y⁸
• 9y⁶
• 6y⁸
• 6y⁶

Multiple Choice

• a
• b

​Dividing with Exponents

What do I do? ​

Subtract exponents.

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Ask yourself the question, how many more x's do I have on top of my fraction or the bottom, that is the same as subtracting. ​

Some text here about the topic of discussion

Multiple Choice

Evaluate the expression using the quotient rule.

• x¹³
• x⁵
• x³⁶
• x^-5

Multiple Choice

$$\frac{8^8}{8^4}$$  

• $$8^4$$  

• $$8^{12}$$  

• $$16^4$$  

Multiple Choice

Simplify

$$\frac{24k^9}{6k^4}$$  

• $$4k^5$$  

• $$6k^5$$  

• $$4k^6$$  

• $$18k^{14}$$  

Multiple Choice

$$\frac{6^4}{6^3}$$  

• $$6^7$$  

• $$6^1$$  

• $$12^1$$  

Multiple Choice

$$\frac{9^4}{9^2}$$  

• $$9^6$$  

• $$18^6$$  

• $$9^2$$  

​Negative Exponents

What do I do?​

Before solving, always make exponents positive. If they are in the numerator, bring them to the denominator, if they are in the denominator, bring them to the numerator.

Some text here about the topic of discussion

Multiple Choice

Which of the following is equivalent to the expression $$g^{-7}$$  ?

• $$g^7$$  

• $$-g^7$$  

• $$\frac{1}{g^7}$$  

• $$-\frac{1}{g^7}$$  

Multiple Choice

Simplify. Your answer must contain only positive exponents. $$s^{-5}s^{-2}$$  

• $$s^{-7}$$  

• $$\frac{1}{s^{10}}$$  

• $$\frac{1}{s^7}$$  

Multiple Choice

(y⁹)^-2

• y¹⁸
• y¹¹
• 1/y¹⁸
• y⁹/2

Multiple Choice

Simplify. Your answer must contain only positive exponents. $$7a^{-5}b^3$$  

• $$\frac{7b^3}{a^5}$$  

• $$\frac{b^3}{7a^5}$$  

• $$\frac{1}{7a^5b^3}$$  

• $$-\frac{7b^3}{a^5}$$  

Multiple Choice

Simplify. Your answer must contain only positive exponents.    $$\frac{10h^0}{2h^{-7}}$$  

• $$\frac{10}{2h^{-7}}$$  

• $$5h^7$$  

• $$\frac{5}{h^7}$$  

• $$\frac{-5}{h^7}$$  

Multiple Choice

Simplify. Your answer must contain only positive exponents.    $$\frac{x^{-4}}{y^{-2}}$$  

• $$\frac{y^2}{x^4}$$  

• $$x^4y^2$$  

• $$\frac{y^{-2}}{x^{-4}}$$  

• $$-\frac{y^2}{x^4}$$  

Lets Combine all the rules and practice now

​Multiply whole numbers when needed

Remember to make everything positive ​

Multiple Choice

Simplify. Hint: do product rule first, then negative rule!

• $$42x^5$$

• $$\frac{42}{x^5}$$

• $$\frac{42}{x^{-5}}$$

• $$\frac{1}{42x^5}$$

Multiple Choice

$$2nm^3\cdot3m^{-2}n^4$$  

• $$-6m^3n^2$$  

• $$6mn^5$$  

• $$-\frac{n^2}{m^2}$$  

• $$-6m^5n^5$$  

Multiple Choice

$$\frac{1}{x^3y^{-2}a^0}$$  

• $$\frac{y^2}{x^3\cdot0}$$  

• $$\frac{x^3}{y^2}$$  

• $$\frac{y^2}{x^3}$$  

• $$1$$  

Multiple Choice

  $$\left(\frac{3x^3}{3xy^2}\right)^2$$  

• $$3xy$$  

• $$\frac{x^6}{y^4}$$  

• $$x^4y^4$$  

Multiple Choice

$$\left(\frac{4^{-2}x^3y^4z^{-5}}{20y^5z^2}\right)$$  

• $$\frac{16x^3y}{20z^7}$$  

• $$\frac{x^3}{320yz^7}$$  

• $$\frac{16x^3}{20yz^7}$$  

• $$\frac{320x^3}{yz^3}$$  

Multiple Choice

$$y^{-2\ \ }y^3\ y^{-3}$$  

• $$y^3$$  

• $$y^2$$  

• $$\frac{1}{y^2}$$  

• $$y^5$$