Chapter 1 Part 1
Exponents, Scientific Notation
and roots
Exponents, Scientific Notation
and roots
Any number to the zero power is 1.
Steps: Recognize that any nonzero number raised to the zero power equals 1.
Evaluate: 90
1
To write a number in scientific notation, express it as a×10n where .
Steps: Move the decimal so only one nonzero digit is to its left. Count the number of places moved; this is n. Write the number as a×10n.
Write 45,000 in scientific notation.
4.5×104
Solving Multi-Step Equation with Variables on One Side
Rule: Isolate the variable by performing inverse operations step by step.
Solve for x:
3x + 7 = 22
x = 5
Multi-Step Equation with Parentheses and Like Terms
Rule: Apply the distributive property, combine like terms, and isolate the variable.
Solve for z:
2(z + 3) + 4z = 24
z = 3
The square root of a number is a value that, when multiplied by itself, gives the original number.
Steps: Think of what number times itself equals the number under the square root.
Find square root of 81
9
To raise a power to a power, multiply the exponents.
Steps: Keep the base the same. Multiply the exponents together. Write the base with the new exponent.
Simplify: (42)3
46 or 4096
Multi-Step Equation with Distribution
Rule: Use the distributive property first, then combine like terms and solve for the variable.
Solve for y:
2(y + 4) - 3 = 13
y = 4
Multi-Step Equation with Multiple Variables and Distribution
Rule: First use the distributive property, then get all variable terms on one side and solve.
Solve for y:
2y + 6 = 4(y - 2) + 2y
y = 3.5
The square root of a decimal is the value that, when multiplied by itself, gives the decimal.
Steps: Think of what decimal times itself equals the number under the square root.
Find square root of 0.25
0.5
To multiply powers with the same base, add the exponents.
Steps: Identify the base. Add the exponents together. Write the base with the new exponent.
Simplify: 23 x 24
27 or 128
Multi-Step Equation with Variables on Both Sides
Rule: Move all variable terms to one side and constants to the other, then solve.
Solve for m:
4m - 5 = 2m + 13
m = 9
Multi-Step Equation with Multiple Variables and Fractions
Rule: Get rid of the fractions by multiplying both sides by the least common denominator, then collect variable terms on one side.
Solve for n:
3/4n+ 7 = 1/4n + 15
n = 16
The cube root of a number is a value that, when used three times in multiplication, gives the original number.
Steps: Think of what number multiplied by itself three times equals the number under the cube root.
Find the cube root of 64
4
To multiply numbers in scientific notation, multiply the coefficients and add the exponents of 10.
Steps: Multiply the numbers in front (coefficients). Add the exponents of 10. Write as a×10n.
Simplify: (3×104)×(2×103)
6×107
Multi-Step Equation with Multiple Variables on Both Sides
Rule: Collect all terms with the variable on one side and all constants on the other side.
Solve for x:
5x + 8 = 3x + 20
x = 6
Multi-Step Equation with Decimals
Rule: Combine like terms and isolate the variable. Work carefully with decimal numbers.
Solve for k:
1.5k - 4 = 8.5
k = 8.333 or 8 1/3
To divide powers with the same base, subtract the exponents.
Steps: Identify the base. Subtract the exponent of the denominator from the exponent of the numerator. Write the base with the new exponent.
Simplify: 56 / 52
54 or 625
To divide numbers in scientific notation, divide the coefficients and subtract the exponents of 10.
Steps: Divide the numbers in front (coefficients). Subtract the exponent in the denominator from the exponent in the numerator. Write as a×10n.
Simplify: (8×107)÷(2×103)
4×104
Word Problem: Buying Game Cards
Rule: Write an equation based on the situation and solve for the unknown.
Jamal bought 3 packs of game cards and paid \$5 for shipping. The total cost was \$29. How much did each pack of game cards cost?
Let p represent the price of one pack.
Equation: 3p + 5 = 29
p = 8
Word Problem: Allowance
Rule: Translate the word problem into an equation, then solve step by step.
Sarah earns \$15 each week for chores and gets an extra \$2 for every time she washes the dishes. If she earned \$29 in one week, how many times did she wash the dishes?
Let d represent the number of times Sarah washed the dishes.
Equation: 15 + 2d = 29
d = 7