Chapter 4 Study Guide

7th Grade Accelerated Math

What is the following expression simplified? 18x⁸y⁹/6x²y⁵

3x⁶y⁴

What is the product of (5a²b²) and (2a⁴b²)?

10a⁶b⁴

Which of the following numbers is the least?

3.2, √11, √13, 3.61

√11

The Statue of Liberty weighs 450,000 pounds. What is this number written in scientific notation?

4.5 • 10⁵

What two integers are closest to √41?

6, 7

Evaluate x² + 16yˉ³ if x = 3 and y = 2.

11

Evaluate 8⁰ + 4³.

65

Evaluate ³√8.

2

Find the product of 4ˉ⁶ and 4⁸ in exponential form.

4²

Simplify (√225)².

225

Estimate ³√130 to the nearest whole integer.

5

Solve for x as a positive number: x² = 400

20

Solve for x as a negative number: x² = 400

-20

How many inches is the side of a square that has an area of 64 square inches?

8

Compare -√70 and -³√1000 using

>

Which of the following numbers is the greatest? √24, 4 √7

√24

Which of the following numbers is the least? √24, 4 √7

√7

How is the expression 4ˉ² written using a positive exponent?

1/4²

Rewrite 1/m⁸ as a negative exponent.

mˉ⁸

Simplify 2²m • 2²m.

2

Solve for y: y³ = 216

6

What is the simplified form of the expression (2x⁴)(-3x³)?

-6x⁷

Using exponents, what is the simplified form of the expression 15x⁶/3x²?

5x⁴

The diameter of the Earth is approximately 1.28 • 10⁴. Write this number in standard form.

12800

The thickness of a human hair is 0.000012 meters. Write this thickness in scientific notation.

1.2 • 10ˉ⁵

(4.2 • 10²)(2 • 10³)

8.4 • 10⁵

Numbers that can be written as a fraction are called what?

rational

Numbers that cannot be written as a fraction are called what?

irrational

What category of numbers features negative and positive whole numbers?

integers

Simplify: (1/2m³n⁴)(-10mn⁵)(2m⁴n)

-10m⁸n^10

Simplify: (2x³y²)(-4xy⁴)

-8x⁴y⁶

Simplify: -5z⁴w⁷/z⁶wˉ² with positive exponents.

-5 1/z²w⁹

Evaluate the following expression. Write the answer as a negative exponent. 10⁶ ÷ 10

10ˉ⁷

Evaluate the following expression. Write the answer as a positive exponent. 10⁶ ÷ 10

1/10⁷

Evaluate the following expression. Write the answer as a decimal. 10⁶ ÷ 10

0.0000001

What is the counting numbers from this list? -9, √16, 0, 5.2, 0.5, √71, 3π, 12.03789...

√16

What is the whole numbers from the list? -9, 0, 5.2, 0.5, √71, 3π, 12.03789...

0

What is the integer from this list? 5.2, 0.5, √71, 3π, 12.03789... 12

12

What is the irrational number from this list? -9, √16, 0, 5.2, 0.5, 3π, 12?

3π

Find the sum: (9.6 • 10ˉ³) + (4.7 • 10ˉ²)

451.2 • 10ˉ³

Find the difference: (8 • 10⁵) - (5.3 • 10⁴)

7.47 • 10⁵

The top speed of a cheetah is approximately 1.2 • 10² kilometers per hour, while the speed of the fastest human is approximately 4 • 10¹ kilometers per hour. How many times faster is the top speed of a cheetah than the speed of a human?

3 • 10^-1

Round 4.789 to the nearest hundredth.

4.79

Find the value of 6x - w if x = 2 and w = -5.

17

-7/12 + -1/12 = ? Reduce fully.

-213

(-5 - 6)(-42 ÷ 6) = ?

-77

Solve for y: 5y = 3y + 10

5

Which of the following numbers is the greatest? 3.2, √11, √13, 3.61

3.61