Laws of Exponents

Multiplying

100

Find the area of rectangle with length 4x² and width 5x³ 

20x⁵

200

Find the perimeter of a square with with length (2x)³

32x³

300

If z=(-2)⁴ , What is: z²  as an exponential expression

(-2)⁸        (-2)⁴ x (-2)⁴

400

If z=(-2)⁴ , What is the value of z²

256

500

(-2x⁵y³z²)³(4x²y⁵z)

-32x¹⁷y¹⁴z⁷

Dividing

100

What is the value of x⁵/x³ if x = 7

49

200

What is x⁷y^-3z^-9 / x^-11y^-8x⁵

x¹⁸y⁵z^{-14     or}   x¹⁸y⁵/z¹⁴

300

2^-3x³y/2^-3xy²

x²y^-1   or x²/y

400

2x²/x⁴

^{positive exponent}

What is 2/(x²)

500

(3.5 x 10⁸) / (7 x 10⁴)

scientific notation

5 x 10³

Exponent of Exponent

100

(a²)³

What is a⁶

200

(ab³)⁵

What is a⁵b¹⁵

300

The side length of a cube is (14x⁵) What is the volume?

14³x¹⁵

400

What is (16x⁸z^-6)^1/2

Give best answer

4x⁴z^-3    or     4x⁴/z³

500

27^4/3 +  (144^1/2)

81 + 12 = 93

Negative Exponents

100

x^-1

positive exponent

What is 1/x

200

1/x^-3

positive exponent

x³

300

2x^-2

positive exponent

What is 2/x²

400

(x^-2y⁴)^-3

^{positive exponent}

x⁶/y¹²

500

(2/3)^-3 + (1/5)^-2

What is the value?

28 3/8

Mixed Bag

100

Mr.    Griffin’s    class    is    studying    the    solar    system.        The    circumference    of    the    Earth    at    the    equator is     about    249,000    miles.        Express    this    number    in    scientific    notation.

2.4 x 10⁵

200

final answer in exponent form 15⁷ x 4⁷

60⁷

300

Simplify    8^1/5 x 4^1/5

2

400

    The    population    of    the    United    State    is    3×10⁴  and    the    population    of    the    world    is  9 ×10⁹.        How    many     times    larger    is    the    population    of    the    world    than    the    U.S.?

3 x 10⁵

500

A    speck    of    dust    in    an    electron    microscope    is    1.2 × 10² millimeters    wide.        The    image    is    5×10³  times    larger    than    the    actual    size.        How    many    millimeters    wide    is    the    actual    speck    of    dust?

2.4 x 10^-2