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Product & Quotient Rules of Exponents
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• Slide 1
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Product & Quotient Rules of Exponents

Laws of Exponents

• Slide 2
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Product Rule

• Look at the right and see what happens when you multiply powers that have the same base

• When you expand 32 you have two 3s being multiplied and when you expand 33 you have three 3s being multiplied.

• All together how many 3s are you multiplying?

• Slide 3
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Product Rule Short Cut?!!

When you multiply same base powers you keep the base and add the exponents.

x2 * x7 = x2+7 = x9

• Question 4
30 seconds
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Q.

Simplify the following:

$a^{11}\cdot a^2\cdot a^0$

$a^{13}$

$1$

$a^{22}$

$a^0$

• Question 5
30 seconds
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Q.

Simplify the following:

$x^3\cdot y^2\cdot x^2$

$xy^7$

$x^5y^2$

$\left(xy\right)^7$

$x^5$

• Question 6
30 seconds
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Q.

Simplify the following:

$x^3\cdot x\cdot x^{-2}$

$x^1$

$x^5$

$x^6$

$x^2$

• Slide 7
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Quotient Rule

• When dividing powers that have the same base think of dividing as the inverse of multiplying, so what is the inverse of adding?

• When you expand x5 you have five Xs being multiplied in the numerator and when you expand x2 you have two Xs being multiplied in the denominator.

• So what happens when you have the Xs in the numerator and Xs in the denominator? Yup! you cross out the matching pairs!

• Now what did you end up with?

• Slide 8
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Quotient Rule Short Cut?!!

When you divide same base powers you keep the base and subtract the exponents.

x7 / x2 = x7-2 = x5

• Question 9
30 seconds
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Q.

Simplify the following:

$\frac{x^{16}}{x^2}$

$x^{14}$

$x^8$

$x^{18}$

$x^{-8}$

• Question 10
30 seconds
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Q.

Simplify the following:

$\frac{x^9y^7}{x^2y^6}$

$xy^8$

$\left(xy\right)^{24}$

$x^7y$

$x^{11}y^1$

• Question 11
30 seconds
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Q.

Simplify the following:

$\frac{x^7}{x^{-4}}$

$x^{11}$

$x^3$

$x^{-3}$

$x^{-11}$

• Question 12
30 seconds
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Q.

Simplify the following:

$\frac{x^3}{x^8}$

$x^{-5}$

$x^5$

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

$\frac{1}{x^{11}}$

• Question 13