Exponent Notation 1

Question 1 of 5

Simplify

$y xx y xx y xx y xx y xx y$

1. $6y^6$
2. $y$
3. $6y$
4. $y^6$

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Product of Powers

${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$

Notice the bases are the same $(y)$ .

Since we are multiplying the bases, add the powers.

Any base without a power means to the power of

$1$ .

	$y xx y xx y xx y xx y xx y$
$=$	$\color{#00880A}{y}^1 \times \color{#00880A}{y}^1 \times \color{#00880A}{y}^1 \times \color{#00880A}{y}^1 \times \color{#00880A}{y}^1 \times \color{#00880A}{y}^1$
$=$	$\color{#00880A}{y}^{1+1+1+1+1+1}$	Use the Product of Powers
$=$	$y^6$

$y^6$

Question 2 of 5

Simplify

$2 xx 2 xx 2 xx 2 xx a xx a xx a$

1. $8a^2$
2. $4a^4$
3. $16a^3$
4. $6a^3$

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Mute

Product of Powers

${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$

Using the Product of Powers, bring similar bases together.

Remember that any base without a power means to the power of

$1$ .

		$2 xx 2 xx 2 xx 2 xx a xx a xx a$

	$=$	$2^1$ $xx$ $2^1$ $xx$ $2^1$ $xx$ $2^1$ $xx$ $a^1$ $xx$ $a^1$ $xx$ $a^1$

	$=$	$\color{#00880A}{2}^{1+1+1+1} \times \color{#9a00c7}{a}^{1+1+1}$

	$=$	$\color{#00880A}{2}^4 \times \color{#9a00c7}{a}^3$

	$=$	$2^4 a^3$

Simplify further by changing

$2^4$ to its full value.

	$=$	$2^4 a^3$
	$=$	$(2xx2xx2xx2)a^3$
	$=$	$16a^3$

$16a^3$

Question 3 of 5

Simplify

$f xx f xx f xx 5f$

1. $5f^4$
2. $5^4f^4$
3. $4f$
4. $5^4f$

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Mute

Product of Powers

${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$

First, separate the numbers and the variables.

		$f xx f xx f xx 5f$
	$=$	$f xx f xx f xx 5 xx f$

Next, using the Product of Powers, bring similar bases together.

Remember that any base without a power means to the power of

$1$ .

		$f xx f xx f xx 5 xx f$

	$=$	$f^1$ $xx$ $f^1$ $xx$ $f^1$ $xx$ $5^1$ $xx$ $f^1$

	$=$	$\color{#00880A}{f}^{1+1+1+1} \times \color{#9a00c7}{5}$

	$=$	$\color{#00880A}{f}^4 \times \color{#9a00c7}{5}$

	$=$	$5f^4$

$5f^4$

Question 4 of 5

Simplify

$p xx q xx p xx q xx p$

1. $p^3 q^2$
2. $pq^5$
3. $p^5q$
4. $p^2q^3$

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Product of Powers

${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$

First, put the same bases together.

		$p xx q xx p xx q xx p$
	$=$	$p xx p xx p xx q xx q$

Next, using the Product of Powers, bring similar bases together.

Remember that any base without a power means to the power of

$1$ .

		$p xx p xx p xx q xx q$

	$=$	$p^1$ $xx$ $p^1$ $xx$ $p^1$ $xx$ $q^1$ $xx$ $q^1$

	$=$	$\color{#00880A}{p}^{1+1+1} \times \color{#9a00c7}{q}^{1+1}$

	$=$	$\color{#00880A}{p}^3 \times \color{#9a00c7}{q}^2$

	$=$	$p^3 q^2$

$p^3 q^2$

Question 5 of 5

Simplify

$7 xx s xx s xx s xx 2$

1. $9s^3$
2. $2s^4$
3. $7s^4$
4. $14s^3$

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Product of Powers

${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$

First, bring like terms together.

		$7 xx s xx s xx s xx 2$
	$=$	$7 xx 2 xx s xx s xx s$

Next, using the Product of Powers, bring similar bases together.

Remember that any base without a power means to the power of

$1$ .

		$7 xx 2 xx s xx s xx s$

	$=$	$7^1$ $xx$ $2^1$ $xx$ $s^1$ $xx$ $s^1$ $xx$ $s^1$

	$=$	$\color{#00880A}{14} \times \color{#9a00c7}{s}^{1+1+1}$

	$=$	$\color{#00880A}{14} \times \color{#9a00c7}{s}^3$

	$=$	$14s^3$

$14s^3$

Exponent Notation 1

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Quiz summary

Information

1. Question

Hint

Well Done!

Product of Powers

2. Question

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Great Work!

Product of Powers

3. Question

Hint

Correct!

Product of Powers

4. Question

Hint

Keep Going!

Product of Powers

5. Question

Hint

Well Done!

Product of Powers

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