Unit 1: Exponents and Equations Study Guide

Ace your 8th grade math exam! This study guide covers exponents, scientific notation, and rational numbers.

Use the ^ (shift 6) to represent the exponent. Leave the answer in terms of a negative exponent.Simplify (x 3 ) -4 x3 x ^-9 Write your answer in standard form.Simplify 42* 4-3 1 Use ^ (shift 6) to represent the exponent.Which expression is equivalent to (x4)-5 x^ -20 Solve for x. x2=64 x=8 Solve for x. x3=64 x=4 What is the √121? 11 If the volume of the cube is 125 units, what is the length of side x ? x=5 About how many times greater is 12,000 miles than 3 • 103 miles? 4 times as great Use* (shift 8) to represent multiplication and ^ (shift 6) to represent the exponent. Write your answer in scientific notation.Evaluate. (1.5 • 105)(3.18 • 1011) 4.77 * 10^16 Evaluate 83 512 Look at the number line.Which is the best explanation for why point X is a good estimate for √72? 8*9=72 √72 is somewhere between 7 and 10. 82 = 64 and 92 = 81, and point X is at about 8.5. 102= 100 ,and point X represents a number that is less than 100. Which is an irrational number? 7 1.8 22 9.146592017492403… Graph the numbers √5, 1.7, √25, ½, and π on a number line. Then, order the numbers from least to greatest. The table shows estimates of astronomical distances. The distance from Earth to the moon is 383,000 km. The distance from Earth to the sun is 1 AU. About how many times farther is Earth from the sun than it is from the moon? Write your answer in scientific notation, and round the decimal part of your answer to two decimal places. Earth is about 2.61 × 103times farther from the sun than it is from the moon. Earth is about 2.61 × 106 times farther from the sun than it is from the moon. Earth is about 2.61 × 101times farther from the sun than it is from the moon. Earth is about 2.61 × 108 times farther from the sun than it is from the moon. Which of the following is a rational number? the square root of a prime number. the length of a side of a square with an area of 25cm2 the non-terminating, non-repeating decimal. the length of the side of a square with an area of 5cm2 . Zach is learning about rational and irrational numbers. What conclusion can he draw about the number 0.01011011101111011111...? It is rational because it repeats. It is rational because it terminates. It is irrational because it neither repeats nor terminates. It is irrational because it repeats. An astronomer wrote the distances from Earth to two different stars in scientific notation.Distance from Earth to star A = 4 × 1013Distance from Earth to star B = 8 × 1015About how many times farther from Earth is star B than star A? 2 10 100 200 On a number line, √6 would fall between… 2.1 and 2.2 2.4 and 2.5 2.8 and 2.9 3.1 and 3.2 Estimate √47 to the nearest tenth. 24.5 23.5 6.9 6.5 Match the point on the number line to the square root below. √40 √30 √11 √5.5 Jacqulyn sewed 115 fabric squares for her new quilt. Each fabric square was 12 inches by 12 inches. If no fabric square was cut or folded, which statement describes the largest square quilt Jacqulyn could make? Jacqulyn has too many squares for a 9-foot-by-9-foot quilt and not enough squares for a 10-footby-10-foot quilt. Jacqulyn has too many squares for a 10-foot-by-10-foot quilt and not enough squares for an 11- foot-by-11-foot quilt. Jacqulyn has too many squares for an 11-foot-by-11-foot quilt and not enough squares for a 12- foot-by-12-foot quilt. Jacqulyn has too many squares for a 12-foot-by-12-foot quilt and not enough squares for a 13-footby-13-foot quilt. Use commas in your answer.What is 2.35 • 104 In standard form? 23,500 Solve for x. Write your answer in simplest form. 1 Estimate.Which two whole numbers √425 is between. Why did you choose these two numbers? 20 and 21 Anzayviah is playing a game in math class where the students describe a number they are thinking of and the class uses clues to determine which type of number it is. Anzayviah tells her class that she is thinking of a positive number with infinitely many nonrepeating digits after the decimal point. Which type of number is Lyla thinking of? A(n)irrational number