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Level 282

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2⁻¹

½

2⁻³

⅛

2⁻²

¼

2⁰

1

3⁻¹

⅓

(-1)²³

-1

(-1)³²

1

-5²

-25

(-5)²

25

5⁻²

1/25

3⁻²

1/9

(-2)⁰

1

-2⁰

-1

1⁻⁵

1

-1⁵

-1

2⁻⁴

1/2⁴

2⁻⁵

1/32

x⁵⋅x

x⁶

p³/p⁷

p⁻⁴ or 1/p⁴

(2a³)(5a⁶)

10a⁹

(−c⁴)(3c²)

-3c⁶

(−x⁷)(x⁻²)

-x⁵

(−4m)(−3m)

12m²

p⁷/p³

p⁴

c⁹⋅c⁻⁴

c⁵

3u²⋅8u⁶

24u⁸

c⁻⁹⋅c⁴

Either c⁻⁵ or 1/c⁵

a⁷/a⁷

1

a⁶⋅a⁶

a¹²

a⁷⋅a⁻⁷

1

(−3d)(5d⁵)(−d³)

15d⁹

c⁶/c³

c³

c³/c⁶

Either c⁻³ or 1/c³

1⁻⁸

1

(-1)⁸

1

0⁴

0

5/x

Express without using a negative exponent: 5x⁻¹

1/(5x)

Express without using a negative exponent: (5x)⁻¹

4/n²

Express without using a negative exponent: 4n⁻²

1/(16n²)

Express without using a negative exponent: (4n)⁻²

(3x³)²

9x⁶

(2a³)⁵

32a¹⁵

(-10p³)⁴

10,000p¹²

(-10p⁴)³

-1000p¹²

(-x²y³)⁵

-x¹⁰y¹⁵

(-x²y)⁴

x⁸y⁴

(-3w³)²

9w⁶

(-3w²)³

-27w⁶

(½)⁻³

8

(⅜)⁻²

64/9

(¾)⁻³

64/27

(1/10)⁻⁵

10,000

(10xy⁵)/(-2x⁸y²)

Either -5x⁻⁷y³ or -5y³/x⁷

(3a²b)/(6ab)

a/2

(5mn)/(10m²n³)

Either 1/(2mn²) or ½ m⁻¹n⁻²

(-3)⁻²

1/9

(-10)⁻³

-1/1000

2x²

3x² - x²

2x³y² + 5x⁵y⁶

Can't simplify further

16x²y³

5x²y³ + 11x²y³

7a + 7a²

Can't simplify further

(2a³)³/(4a)

2a⁸

Product of Powers Property

Example: 2² * 2³ = 2²⁺³

Example: (2³)² = 2³*²

Power of a Power Property

Power of a Product Property

(ab)^x = a^x * b^x

Negative Exponent Property

a non zero base raised to a negative exponent is equal to the reciprocal of the base raised to the oppositive positive exponent. a^-m = 1/a^m

Zero Exponent Property

any number raised to the zero power = 1

Quotient of Powers Property

to divide powers WITH THE SAME NON ZERO BASE, subtract the exponents a^m/a^n = a^m-n

Power of a Quotient Property

(a/b)^m = (a^m) / (b^m) when b is not zero

Linear Function

y = mx + b

Exponential Function

y = ab^x

power

a number produced by raising a base to an exponent

Expanded Form of Exponents

Expanded form utilizes the fact that exponents represent how many times the base is being multiplied. y to the 5th power (y^5) in expanded form is y*y*y*y*y.

Power Rule of Exponents

When multiplying expressions with the same base, you can add the exponents. For example, (x^2)*(x^4) = x^6. This works because you have (x*x)(x*x*x*x) which is 6 x's all multiplied.

Negative Power Rule for Exponents

When taking a number or variable to a negative exponent, it is the opposite of multiplication, which means we divide. For example, 5^-3 is the same as 1/5^3, which is 1/125. We divide by 5 three times.

Negative Power Rule for Fractions

When we take a fraction to a negative exponent, the numerator switches from multiplication to become division on the denominator. The denominator likewise turns into multiplication on the numerator. For example, (3/4)^-3 turns into (4^3)/(3^3) = 64/27.

Zero Rule for Exponents

Anything to the 0 exponent is 1. This is because we are neither multiplying or dividing by the term. For example, (3xy)^0 = 1.

Rule for Fractional Exponents

A fractional exponent can be rewritten into radical form. The root of the radical is the same as the denominator of the fraction. For example, 8^(3/2) is the same as the square root of 8^3.

Express without using a negative exponent: 5x⁻¹

5/x the 5 stays where it is. move the factor that has the negative exponent

Express without using a negative exponent: (5x)⁻¹

1/(5x) the ( ) tells you the whole thing moves to the bottom

Express without using a negative exponent: 4n⁻²

4/n² the 4 has a positive 1 as a exponent. It stays on top.