How to divide exponents
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PSAT Math › How to divide exponents
If 
Cannot be determined
Explanation
Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.
Explanation
The key to this problem is understanding how exponents divide. When two exponents have the same base, then the exponent on the bottom can simply be subtracted from the exponent on top. I.e.:
Keeping this in mind, we simply break the problem down into prime factors, multiply out the exponents, and solve.
Simplify
None
Explanation
Divide the coefficients and subtract the exponents.
54 / 25 =
25
5
10
50
54 / 5
Explanation
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.
a3(b3√b)(c)
(b3)/(a3c2)
(b3√b)/(a3c)
(b7)/(a3c)
a2b3√c
Explanation
For all real numbers n, (2_n_ * 2) / (2_n_ * 2_n_) =
2_n_/2_n_
2_n_
21 – n
2_n_ – 1
2
Explanation
(2_n_ * 2) / (2_n_ * 2_n_) simplifies to 2/2_n_ or 21/2_n_.
When dividing exponents with the same base, you subtract the divisor from the dividend, giving 21–n.
Simplify the following expression: (x2y4)/(x3y3z2)
xy/z2
xz2/y
y/xz2
z2xy
Explanation
According to the rules of exponents, ax/ay = ax-y
In this expression, we can follow this rule to simplify x2/x3 and y4/y3
x2–3 = x–1 = 1/x. y4–3 = y1 = y.
Therefore, y/xz2
Half of the radioactive nuclei of a substance decays in a week. If a sample started with 1010 nuclei, how many have decayed after 28 days?
9.375 x 109
1010
106
6.25 x 108
28 x 1010
Explanation
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
If x7 / x-3/2 = xn, what is the value of n?
10/2
21/2
-21/2
11/2
17/2
Explanation
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+3/2 due 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
Since x7 / x-3/2 = xn, xn = x17/2
So n = 17/2
- 5. Simplify the problem (x4y2/x5)3
x3y6
x4/y6
y6/x3
y5/x
x/y
Explanation
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).