Basic Exponents
(-7)3
Steps: -7 * -7 * -7
49 * -7
Answer = 343
Everything inside the parentheses gets the power!!
Question: (23)2
Steps:
23*23
Answer = 26
Anything raised to the zero power is 1.
x0=1
Question: (3x)0
Steps:
(3x) canceled out, leaving it 0
Answer = 1
LARS —> If you move the decimal LEFT, then you ADD to the exponent! If you move the decimal RIGHT, then you SUBTRACT to the exponent!
Question: 25,600
Steps:
1. Starting the decimal after the 0, you move it to the left 4 places.
2. Equalling; 2.56, and because you move to the left 4 places, it equals; 104.
Answer= 2.56*104
√12
Steps: √4 * √3
=2√3
x7*x5
Add exponents!
Steps:
x7 * x5
Answer =x12
(x6/y9)3
Steps:
1. x6*x6*x6= x18
2. y9*y9*y9= y27
Answer= x18/y27
5x0
Steps:
Because there are no parentheses around 5x, the x0 is canceled out
Answer= 5
0.000000832
Steps:
1. Starting from the decimal point, move it to the right 7 times, equalling; 8.32.
2. Because you moved it to the right, “If you move the decimal RIGHT, then you SUBTRACT to the exponent”, equalling; 10-7.
Answer= 8.32*10-7
√50
Steps: √25 * √2
= 5√2
(3a9)(6a-4)
Steps:
1. 3*6= 18
2. a9+a-4= a5
Answer = 18a5
(-5/a4)3
Steps:
1. -5*-5*-5 = -125
2. a4*a4*a4= a12
Answer = -125/a12
(50a5b0)7
Steps:
1. 50, and b10 are cancelled out
2. (a5)7
Answer= a35
You can only add or subtract if the exponents are the SAME!
Question: 1.75x104 + 7.8x104
Steps:
1.) 1.75+7.8= 9.55
2.) You keep the exponent of 104.
Answer: 9.55*104
√125
steps: √25 * √5
=5√5
(2x3y)(-9x8y3)
Steps:
1. 2 * -9 = -18
2. x2 * x8 = x10
3. y * y3 = y4
Answer = -18x10y4
(3x4y6)4
Steps:
1. 3*3*3*3= 81
2. x4*x4*x4*x4= x16
3. y6*y6*y6*y6= y24
Answer= 81x16y24
A negative exponent NEVER makes a number negative!
x-a= 1/xa
Question: (a2b)-1
Steps:
Because the problem has parentheses, and it’s negative, the -1 is made positive, and put as the numerator, while the a2b is made the denominator.
Answer= 1/a2b
3.81x105 + 4.05x106
Steps:
1. Because the exponents aren’t the same, you have to make them the same, by adding +1 to 105, equaling; 3.81*106+4.05*106
2. Because you added +1, you have to move the decimal place to the left, (LARS), equaling; 0.381*106+4.05*106.
3. Adding 0.381+4.05= 4.431.
Answer= 4.431*106
√675
Steps:
1. √25 √27= 5√27
2. 5√27—> 5√9*√3
3. 5√9*√3–> 5*3√3
=15√3
2/7a5b6 * 4/11b9c4
Steps:
1. 2/7*4/11= 8/77
2. b6*b9= b15
Answer = 8/77a5b15c4
(2x7y2/w-4z10)5
Steps:
1. 2*2*2*2*2= 32
2. x7*x7*x7*x7*x7*x7*x7= x35
3. y2*y2*y2*y2*y2= y10
4. 32x35y10
5. w-4*w-4*w-4*w-4*w-4= w-20
6. z10*z10*z10*z10*z10= z50
7. x-20z50
Answer= 32x35y10/w-20z50
(3x-4y6)-1
Steps:
1. -1 distributes to 3, x-4, and y-6.
2. Equalling; 3-1x4y-6.
3. Because there can’t be any negatives, the 3-1 and y-6 go on the bottom of the equation, and the 3-1 becomes a 3, and the y-6 becomes a y6.
4.
Answer= x4/3y6
6.44*10-2-1.89*10-1
1. Because the exponents aren’t the same, you have to make them the same, by adding +1 to 10-2, equaling; 6.44*10-1-1.89*10-1.
2. Because you added +1, you have to move the decimal place to the left, (LARS), equaling; 0.644*10-1-1.89*10-1.
3. Adding 0.644-1.89= -1.246
Answer= -1.246*10-1
√392
Steps:
1. √49*√8
2. 7*√8—> 7*√4*√2
3. 7*√4*√2—> 7*2*√2
=14 √2