# GMAT QUANT 5

### 154 terms by josie4444

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### (1/2)(b)(h)

Area of a triangle

### A triangle with two equal sides and two equal angles is...

An isosceles triangle

### (b)(h)

(f) Area of a parallelogram

### (π)(r2)

(f) Area of a circle

### (2)(π)(r)

(f) Circumference of a circle

### (l)(w)(h)

(f) Volume of a rectangular solid

### s³

(f) Volume of a cube

### (π)(r2)(h)

(f) Volume of a cylinder

### 180(n-2) n=number of sides

(f) Sum of interior angles of a polygon

### Even exponents always result in...

A positive integer

1

### An exponential expression with a base of -1 =

-1 if the exponent is odd, 1 if the exponent is even

decreases

decreases

aⁿbⁿ

aⁿ + bⁿ

(a+b)ⁿ

nᵃᶧᵇ

nᵃnᵇ

### When can you combine exponents via addition?

When you are multiplying exponential terms with the same base

nᵃ⁻ᵇ

nᵃ/nᵇ

### When dividing two exponential terms with the same base...

Combine exponents by subtracting

### When can you combine exponents via subtraction?

When you are dividing exponential terms with the same base

nᵃᵇ

### When raising a power to a power...

Combine exponents by multiplying

### When can you combine exponents via multiplication?

When you are raising one power by another power

1/nᵃ

nˉᵃ

(m/n)ᵃ = mᵃ/nᵃ

(n/m)ˉᵃ

### A negative exponent implies...

The reciprocal of the base

The base

n

-n

1

1

1

1

Indeterminate

1

### For fractional exponents, the base number is raised to the _______ and taken to the root of the ________.

raise: numerator, root: denominator

ᵇ√(nᵃ) = (ᵇ√n)ᵃ

(ᵇ√n)ᵃ = nᵃ/ᵇ

nᵃʹᵇ = ᵇ√(nᵃ)

xᵃ+ᵇ

(xᵃ)(xᵇ)

c⁹

3⁹

5ⁿ+¹

(ab)ⁿ

(aⁿ)(bⁿ)

6⁴

### 12⁵ = (simplify)

(4⁵)(3⁵) = (2¹⁰)(3⁵)

1/2ˉ⁶ = 2⁶

x⁴

aⁿ/bⁿ

(a/b)ⁿ

10⁶/2⁶ = 5⁶

### 3⁵/9⁵ = (simplify)

(3/9)⁵ = (1/3)⁵ = 3ˉ⁵

(aᵐ)ⁿ = (aⁿ)ᵐ

(3⁵)⁴ = 3²⁰

1/xᵃ

xˉᵃ

(2/3)² = 4/9

2/x⁴

### 27⁴ʹ³ =

³√(27⁴) = (³√27)⁴ = 3⁴ = 81

x¹⁵ʹ³ = x⁵

3aⁿ

3(3⁴) = 3⁵

3(3ⁿ) = 3ⁿ⁺¹

### You can simplify exponential expressions that are linked by...

multiplication or division

### You can simplify exponential expressions linked by multiplication/division if...

they have an exponent or base in common

x² + 2xy + y²

x² - 2xy + y²

nonnegative root

sign

### Describe the numerator and denominator of a fractional exponent

numerator = power raised, denominator = root taken

### You can find the root of a number by...

Breaking the number down into prime factors

### You can simplity roots by combining/separating in...

multiplication or division

### (d) Imperfect square

Square root of the the number is not an integer

### How do you estimate the roots of imperfect squares?

Find the two closest perfect squares. If there is a coefficient, transfer it to under the root before searching for the two closest perfect squares

ⁿ√(x/y)

√2

³√8 = 2

ⁿ√(xy)

√50

³√216 = 6

### ᵇ√xᵃ =

(ᵇ√x)ᵃ = ᵇ(√xᵃ) = xᵃʹᵇ

### 25³ʹ² = (solve)

(√25)³ = 5³ = 125

1/√49 = 1/7

x¹⁵ʹ⁵ = x³

### √(x+y) =

Cannot be simplified

### √x + √y =

Cannot be simplified

### √(x-y) =

Cannot be simplified

### √x - √y =

Cannot be simplified

1

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16

25

36

49

64

81

100

121

144

169

196

225

256

400

625

900

1

1.4

1.7

2.25

2

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9

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15

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25

30

1

8

27

64

125

1

2

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Example: