SAT Math : SAT Mathematics
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Example Questions
Example Question #1 : How To Divide Exponents
Simplify the following expression: (x2y4)/(x3y3z2)
xy/z2
xz2/y
z2xy
y/xz2
y/xz2
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
Example Question #2 : How To Divide Exponents
Simplify:
x6y6z6
(z/x)3 / 2
x9 / z9
x4 / z4
x3z9 / y9
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. Raising this to the 3/2 power results in multiplying the exponents by 3/2: x6 * 3/2/z6 * 3/2 = x9/z9.
Example Question #2301 : Sat Mathematics
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?
6.25 x 108
28 x 1010
106
1010
9.375 x 109
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 #2302 : Sat Mathematics
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5. Simplify the problem (x4y2/x5)3
x/y
y6/x3
x3y6
x4/y6
y5/x
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 #2 : How To Divide Exponents
If x7 / x-3/2 = xn, what is the value of n?
21/2
10/2
-21/2
11/2
17/2
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+3/2 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
Example Question #3 : How To Divide Exponents
Simplify x2x4y/y2x
x5/y
x5/y3
x7y2
y/x5
7xy2
x5/y
1) According to the rules of exponents, one can add the exponents when adding to variables with the same base. So, x2x4 becomes 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/y2 becomes 1/y.
3) When combining these operations, one gets x5/y.
Example Question #3 : How To Divide Exponents
a3(b3√b)(c)
(b3)/(a3c2)
(b3√b)/(a3c)
(b7)/(a3c)
a2b3√c
(b3√b)/(a3c)
Example Question #2305 : Sat Mathematics
54 / 25 =
25
54 / 5
10
50
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.
Example Question #121 : Exponents
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.
Example Question #1 : Exponential Operations
Simplify
None
Divide the coefficients and subtract the exponents.
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