Unit 9 Day 1: Exponent Rules

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Negative Exponents

To make a negative exponent positive do one of the following: If the negative exponent is in the numerator position, shift the power to the denominator position. OR If the negative exponent is in the denominator position, shift the power to the numerator position.

add

To multiply two exponential expressions that have the same base, keep the base and ___ the exponents

multiply

To raise a power to a power, keep the same base and ___ the exponents.

quotient rule

When dividing two powers that have the same base, you can subtract the exponents.

product rule

When multiplying two powers that have the same base, you can add the exponents.

power to a power rule

When you have an exponent raised to another exponent you keep the base and multiply the exponents.

1

a⁷/a⁷

x(x)

x⁸

x(x⁷)

1/x⁴

x⁻⁴

7

√49

square root

An exponent of 1/2 is the same as a

1

10⁰

1/100

10⁻²

√144

12

¼

2^-2

2000x⁶

2x³(10x)³

1/8

2⁻³

-12x²

3x(-4x)

-18x⁴

3x²(x²)(-6)

3/x³

3x⁻³

1

4⁰

5x²

5x⁴/x²

1/125

5⁻³

1/5

5⁻¹

√36

6

exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself.

fraction

A negative exponent indicates that we're dealing with a ____

zero power property

Any nonzero number raised to the power of zero equals 1.

1

Anything raised to the zero power equals

each factor

If a product in parentheses is raised the a power, the parentheses indicate that ___ must be raised to that power.

top

If an element on the bottom of a fraction has a negative exponent it means it belongs on the ____

bottom

If an element on the top of a fraction has a negative exponent it means it belongs on the

coefficient

In the expression 2x, the 2 is called the ___ of x.

base

The number that is multiplied by itself

subtract

To divide two exponential expressions that have the same base, keep the base and ___ the exponents.

-27x⁶

(-3x²)³

25x⁸y²z¹⁶

(-5x⁴yz⁸)²

-5x⁷y³

(10x⁸y⁵)/(-2xy²)

4a

(24a²b) / (6ab)

8x³y³

(2xy)³

32x⁵y⁵

(2xy)⁵

81x⁴

(3x)⁴

27x⁹

(3x³)³

64x¹⁵y³

(4x⁵y)³

x⁵

(x²)(x³)

x¹²

(x⁴)³

6x⁴

-2x(x²)(-3x)

8x⁶

-4x³(-2x³)

-√25

-5

(-8x^6)/y^15

(-2x²y⁻⁵)³

8x⁵

(-2x³)(-4x²)

4x⁶

(-2x³)²


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