Name Algebra 1B problem set
January 30, 2009“More exponent calculations” page 1
More exponent calculations
Today’s lesson reviews exponents and their properties, and will give you more practice using them.
Review summary
Meanings of exponents
- Positive exponents represent repeated multiplication.bn = b · b · ··· ·b (nb’s)
- Powers with exponent 1 are just equal to the base.b1 = b
- Powers with exponent 0 are always equal to 1.b0 = 1
Scientific notation
- Used mainly for very large or very small numbers.
- Numbers may be written as a decimal times a power of 10.2.345 · 109
- On a calculator, E is a symbol for 10^ (Use EE to type this). = 2.345 E 9
- Shift the decimal point to get an ordinary number. = 2,345,000,000
- For negative powers of 10, shift the decimal point to the left.7.8 · 10–5
= 7.8 E -5
= 0.000078
Three exponent properties
- To multiply powers with the same base, add the exponents.bm · bn = bm+n
- When there’s a power to a power, multiply the exponents.(bm)n = bmn
- To multiply powers with different bases but the same exponent,
multiply the bases but keep the exponent.an · bn = (ab)n
Examples using the properties
- x2x5 = x2+5 = x7
- (x2)5 = x2·5 = x10
- x4 · x5 · (x2)3
= x4 · x5 · x6
= x4+5+6
= x15
- v3w3 = (vw)3
- x2 · y9 · (x3)4 · y5
= x2 · y9 · x12 · y5
= x14 · y14
= (xy)14
Review problems
1.Using exponent properties, simplify each of these expressions as much as possible.
a.x4x7
b.(x4)7
c.x · x2 · x3
d.(x2)3 · (x5)4
e.x3x5 + x4
f.a4b3a5b2
g.a2b2 (ab)3
h.r4r – s2s3
i.(x2y4z5) · (x5y3z)
2.Which of the following expressions are equal to x8 ? Circle them.
x4 · x2x3 · x5x4 · x4
x2 · x2 · x2x8 · xx8 · x0
(x2)3(x4)2(x6)2
14 · x418 · x8x8 · y0
(–1)8 · x8–x8(–x)8
3.Decide whether each statement is a correct statement about exponents. Circle true or false.
(Assume that all letters stand for positive whole numbers.)
a.truefalse
b.truefalse
c.truefalse
d.truefalse
e.truefalse
f.truefalse
4.Convert these numbers from scientific notation into ordinary number notation.
a.3.14159 · 108
b2.718 · 10–6
c.1.2345 E -3
d.6.02 E 23 (This is a famous number, it’s the number of atoms in one gram of hydrogen!
e.1.06 E 13(This is our national debt in dollars.)
5.Do these function evaluations without a calculator. Show your work.
Remember, don’t use a calculator. Do the multiplying by yourself.
a.Evaluate f(x) = 4 · 5x when x = 3.
b.Evaluate f(x) = 1000 · (1.06)x when x = 2.
c.Evaluate f(x) = 1000 · (1.06)x when x = 0.
d.Evaluate f(x) = when x = 3.
e.Evaluate f(x) = when x = 4.
6.Do these function evaluations with a calculator. If you get a number in scientific notation, turn it into an ordinary number.
a.Evaluate f(x) = 8.3 · 10x when x = 6.
b.Evaluate f(x) = 500,000 · (1.23)x when x = 40.
c.Evaluate f(x) = when x = 3.Make sure answer agrees with problem 5d.
d.Evaluate f(x) = 2 · when x = 20.
7.Here is a function you might find in an exponential decay problem: y = 486 · ()x.
Complete this input-output table without using the [^] key on your calculator.
y
8.Do the following for the function f(x) = · 2x. Do this without a calculator.
a.Fill in the output column of the input-output table.
b.Graph the points on the grid.
c.Complete the graph by drawing a curve that goes through the points.
x / f(x) /0
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