Lesson 1
Simplify.
{4 x ... x 4}
7 times
47
2x2 • 3x9
6x11
(93)6 =
918
y12 / y12 =
y12-12 = y0 = 1
Let f be a nonzero number.
f-4 = ?
1 / f4
Simplify.
{(-11.63) x ... x (-11.63)}
34 times
(-11.63)34
8a5 • 2y3
16a5y3
48
--
58
(4/5)8
915 x (1 / 915) =
915 / 915 = 915-15 = 90 = 1
671 x 28796-1 =
671/28796 or .0233
Simplify.
{(-1/14) x ... x (-1/14)}
10 times
3x3z • 4x3y
12x6zy
(1132 x 37 x 514)3 =
1136 x 373 x 5112
Simplify the following expression as much as possible.
(410 / 410) x 70 =
1
Compute 33 x 32 x 31 x 30 x 3-1 x 3-2
Simplify.
{x⋅x...x}
185 times
x185
12xy2
-------
3x4y2
4
--
x3
Let x,y,z be numbers.
(x2yz4)3 =
x6y3z12
x41 y15
-- x -- =
y15 x41
x41y15 x41 y15
------- = -- x -- = x0y0 = 1x1 = 1
y15x41 x41 y15
Show that (17.6-1)8 = 17.6-8
By the power to a power rule:
(17.6-1)8 = 17.6-1 x 8 = 17.6-8
By the negative power rule:
(17.6-1)8 = (1/17.6)8 = 18 / 17.68
= 1 / 17.68 = 17.6-8
Simplify.
{x⋅x...x} = xn
______ times
n times
4x5y3
------20x3y4
x2
-----
5y
Let x,y,z be numbers and let m,n,p,q be positive integers.
(xmynzp)q
xmqynqzpq
Let a and b be two numbers. Use the distributive law and then the definition of zeroth power to show that the numbers (a0 + b0)a0 and (a0 + b0)b0 are equal.
(a0 + b0)a0= a0 x a0 + b0 x a0 = a0+0 + a0b0
= 1 + 1 x 1 = 1 + 1 = 2
(a0 + b0)b0 = a0 x b0 + b0 x b0 = a0b0 + b0+0
= 1 x 1 + 1 = 1 + 1 = 2
Since both numbers are equal to 2, they are equal.
Show that (2.8-5 / 2.87) = 2.8-12
2.8-5 = 1/2.85
1/2.85 x 1/2.87 = 1/(2.85 x 2.87) = 1/2.812 = 2.8-12