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HW Properties of Exponents

Last updated over 2 years ago
47 questions

The next topic we are learning involves exponents! Let's see how much you remember...

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Analyze the powers with a base of 3. As the exponent decreases by 1, the numbers on the right are being divided by _______

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According to this pattern, what do you think 3^0 equals?

3^4 = 81
3^3 = 27
3^2 = 9
3^1 = 3
3^0 = _______
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According to this pattern, what do you think 5^0 equals?

5^4 = 625
5^3 = 125
5^2 = 25
5^1 = 5
5^0 = _______
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65^0 =

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Any number to the zero power will always equal _______ .
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Let's keep this pattern going. Now that we know 4^0 = 1 what do you think 4^-1 = ?

4^4 = 256
4^3 = 64
4^2 = 16
4^1 = 4
4^0 = 1
4^-1 = _______
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What do you think 5^-1 equals?

5^4 = 625
5^3 = 125
5^2 = 25
5^1 = 5
5^0 = 1
5^-1 =

Negative exponents tell you to flip the base. You can never have a negative exponent in your answer. If you do, flip it to the denominator to make it positive!

Type in all answers as whole numbers or fractions. No decimals!

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2^0=

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12^-1=

Here's an example similar to #12:

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3^-2=

Simplify completely. Your answer should not have exponents.

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4^-2=
Simplify completely. Your answer should not have exponents.

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(-7)^0=

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0^6=

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*Hint: flip the fraction to make the exponent positive. Then evaluate.

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Hint:

Fraction answers only, no decimals!

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Hint:

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Let's expand and look for a shortcut:
How many 2's are underlined? _______

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Let's expand and look for a shortcut:


How many x's are underlined? _______
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Therefore, we can say,

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Hint: The second y has an invisible exponent of 1

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What's the rule?

Example similar to #33:


Notice how we still multiply the coefficients (3 x 2) but add the exponents.
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Now you try!

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Let's expand and look for a shortcut:
How many 2's are underlined? _______

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Let's expand and look for a shortcut:
How many x's are underlined? _______
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Therefore, we can say:

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Hint: z has an invisible exponent of 1

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What's the rule?

Here's an example similar to #41:

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Now you try!

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Therefore, according to the last example we can say:
So when we divide by the same base we _______ the exponents.
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What's the rule?

Example similar to #46:

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Now you try!

Example similar to #47:

Notice how we still divide the coefficients (15 / 5) but subtract the exponents.
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Now you try!

Below are all the exponent rules you re-learned today.

Copy these down in your notes!