Transcript ELF.01.1 - Reviewing Exponent Laws

ELF.01.1 - Reviewing
Exponent Laws
MCB4U - Santowski
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(A) Review of Exponent Laws
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product of powers: 34 x 36
34 x 36 = 34 + 6  add exponents if bases are equal
quotient of powers: 39 ÷ 32
69 ÷ 62 = 69 - 2  subtract exponents if bases are equal
power of a power: (32)4
(32)4 = 32 x 4
 multiply powers
power of a product: (3 x a)5
(3 x a)5 = 35 x a5 = 243a5  distribute the exponent
power of a quotient: (a/3)5
(a/3)5 = a5 ÷ 35 = a5/243  distribute the exponent
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(B) Review of Zero & Negative Exponent
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Evaluate 25 ÷ 25.
(i) 25 ÷ 25 = 25 – 5 = 20
OR (ii) 25 ÷ 25 = 32 ÷ 32 = 1
Conclusion is that 20 = 1.
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In general then b0 = 1
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Evaluate 23 ÷ 27.
(i) 23 ÷ 27 = 23 – 7 = 2-4
OR (ii) 23 ÷ 27 = 8 ÷ 128 = 1/16 = 1/24
Conclusion is that 2-4 = 1/16 = 1/24
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In general then b-e = 1/be
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(C) Review of Rational Exponent
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We will use the Law of Exponents to prove that 9½ = %9.
9½ x 9½ = 9(½ + ½) = 91
Therefore, 9½ is the positive number which when multiplied by itself gives
9  The only number with this property is 3, or % 9
So what does it mean? It means we are finding the second root of 9
We can go through the same process to develop a meaning to 271/3
271/3 x 271/3 x 271/3 = 27(1/3 + 1/3 + 1/3) = 271
Therefore, 271/3 is the positive number which when multiplied by itself
three times gives 27  The only number with this property is 3, or 3 % 3
or the third root of 27
In general, b1/n = n/ b, or that we are finding
the nth root of b.
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(D) The Rational Exponent m/n
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We can use our knowledge of Laws of
Exponents to help us solve bm/n
ex. Rewrite 323/5 making use of the Power
of powers >>> (321/5)3
so it means we are looking for the 5th root
of 32 which is 2 and then we cube it which
is 8
In general, bm/n = (n /b)m
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(E) Important Numbers to Know
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The numbers
1,4,9,16,25,36,49,64,81,100,121,144 are
important because ...
Likewise, the numbers
1,8,27,64,125,216,343,512,729 are
important because ....
As well, the numbers 1,16,81,256, 625
are important because .....
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(F) Examples
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ex 1. Simplify the following expressions:
(i) (3a2b)(-2a3b2)
(ii) (2m3)4
(iii) (-4p3q2)3
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ex 2. Simplify (6x5y3/8y4)2
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ex 3. Simplify (-6x-2y)(-9x-5y-2) / (3x2y-4) and express
answer with positive exponents
ex 4. Evaluate the following
(i) (3/4)-2
(ii) (-6)0 / (2-3)
(iii) (2-4 + 2-6) / (2-3)
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(F) Examples
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We will use the various laws of exponents
to simplify expressions.
ex. 271/3
ex. (-320.4)
ex. 81-3/4
ex. Evaluate 491.5 + 64-1/4 - 27-2/3
ex. Evaluate 41/2 + (-8)-1/3 - 274/3
ex. Evaluate 3/8 + 4/16 - (125)-4/3
ex. Evaluate (4/9)½ + (4/25)3/2
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(G) Internet Links
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From West Texas A&M - Integral
Exponents
From West Texas A&M - Rational
Exponents
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(H) Homework
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Nelson textbook, p84
Q1-10, 13,16,17
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