Exponents & Scientific Notation Test

Exponents

100

 Write x^-3⋅x^-2 using only positive exponents.

1
--
x⁵

200

Simplify (x⁵)^-3

1
--
x¹⁵

300

Write 3¹⁰ as a product of its prime factors.

3×3×3×3×3×3×3×3×3×3

400

 What is (53)⁴ expressed with positive exponents?

53×53×53×53

500

 Find (x^-8)

1
--
x⁸

Standard Decimal Notation

100

Rewrite 3×10⁵ in standard decimal notation.

300,000

200

Convert 4.083×10³ to standard decimal notation.

4,083

300

What is 9.67×10^-4 in standard decimal notation?

0.000967

400

Express 3.200021×10⁷ in standard decimal notation.

32,000,210

500

Rewrite 3×10^-5 in standard decimal notation.

0.00003

Positive Exponents

100

3¹⁰ X 3¹⁵

3²⁵

200

x¹⁰
---
x³

x⁷

300

(4x³)⁴

16x¹²

400

7⁰

1

500

(x^-4y³)⁴

x^-16y¹²

Products

100

Find the product of (3×10²)⋅(2×10³) in scientific notation.

6×10⁵

200

Calculate (5×10⁴)⋅(4×10²).

2.0×10⁷

300

What is the product of (6.0×10³)⋅(3.0×10⁵)?

1.8×10⁹

400

Multiply (2.5×10^-2)⋅(4.0×10⁶).

1.0×10⁵

500

Determine the product of (1.2×10³)⋅(2.5×10^-1).

3.0×10²

Squares and Cubes

100

What numbers square to 81?

9,−9

200

Determine the numbers that cube to −27.

−3

300

Identify the numbers that square to 196.

14,−14

400

Find all numbers that cube to 216.

6, -6

500

What integers square to 144?

12