年代AT Math : How to divide exponents
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Example Questions
Example Question #1 :How To Divide Exponents
For all real numbersn, (2n* 2) / (2n* 2n) =
2n/2n
2n– 1
2n
2
21 –n
21 –n
(2n* 2) / (2n* 2n) simplifies to 2/2nor 21/2n.
When dividing exponents with the same base, you subtract the divisor from the dividend, giving 21–n.
Example Question #2291 :年代at Mathematics
If x9/x3= xn, solve for n.
9
3
6
12
7
6
When dividing terms with the same base, we can subtract the exponents:
9 – 3 = 6
Example Question #1 :How To Divide Exponents
年代implify the following expression: (x2y4)/(x3y3z2)
xy/z2
y/xz2
z2xy
xz2/y
y/xz2
According to the rules of exponents, ax/ay= ax-y
In this expression, we can follow this rule to simplify x2/x3and y4/y3
x2–3= x–1= 1/x. y4–3= y1= y.
Therefore, y/xz2
Example Question #1 :How To Divide Exponents
年代implify:
x6y6z6
(z/x)3/ 2
x9/ z9
x3z9/ y9
x4/ z4
x9/ z9
When dividing, subtract exponents (xa/xb= x(a – b).) Therefore, the quantity in the parenthesis is: x(4 – (–2))* y(–3 – (–3))* z(–1 – 5)= x6/z6. Raisingthis to the 3/2 power results in multiplying the exponents by 3/2: x6 * 3/2/z6 * 3/2= x9/z9.
Example Question #111 :Exponents
Half of the radioactive nuclei of a substance decays in a week. If a sample started with 1010nuclei, how many have decayed after 28 days?
6.25 x 108
9.375 x 109
1010
28 x 1010
106
9.375 x 109
If half of the sample decays each week: 1/2 is left after one week, 1/4 is left after two weeks, 1/8 is left after three weeks and 1/16 is left after four weeks (28 days.) That means that 15/16 has decayed. 15/16 x 1010= 9. 375 x 109
Example Question #1 :How To Divide Exponents
5. Simplify the problem (x4y2/x5)3
x/y
y6/x3
y5/x
x4/y6
x3y6
y6/x3
Properties of exponents suggests that when multiplying the same base, add the exponents, when dividing, subtract the exponents on bottom from those on top, and when raising an exponent to another power, multiply the exponents. Remember that (x4/x5) = x–1= 1/x; Still using order of operations (PEMDAS) we get the following:(x4y2/x5)3= (y2/x)3= y6/(x3).
Example Question #1 :How To Divide Exponents
If x7/ x-3/2= xn, what is the value of n?
17/2
11/2
21/2
10/2
-21/2
17/2
x7/ x-3/2= x7(x+3/2) based on the fact that division changes the sign of an exponent.
x7(x+3/2) = x7+3/2due to the additive property of exponent numbers that are multiplied.
7+3/2= 14/2 + 3/2 = 17/2 so
x7/ x-3/2= x7+3/2= x17/2
年代ince x7/ x-3/2= xn, xn= x17/2
年代o n = 17/2
Example Question #8 :How To Divide Exponents
年代implify x2x4y/y2x
x7y2
y/x5
7xy2
x5/y
x5/y3
x5/y
1) According to the rules of exponents, one can add the exponents when adding to variables with the same base. So, x2x4becomes x6.
2) The rules of exponents also state that if the bases are the same, one can substract the exponents when dividing. So, x6/x becomes x5. Similarly, y/y2becomes 1/y.
3) When combining these operations, one gets x5/y.
Example Question #1 :How To Divide Exponents
(b7)/(a3c)
a3(b3√b)(c)
(b3√b)/(a3c)
(b3)/(a3c2)
a2b3√c
(b3√b)/(a3c)
Example Question #10 :How To Divide Exponents
54/ 25 =
5
50
25
10
54/ 5
25
25 = 5 * 5 = 52. Then 54/ 25 = 54/ 52.
Now we can subtract the exponents because the operation is division. 54/ 52= 54 – 2= 52= 25. The answer is therefore 25.
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