ACT Math : Exponents
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Example Questions
Example Question #1 : How To Add Exponents
Simplify: hn + h–2n
h–2n = 1/h2n
hn + h–2n = hn + 1/h2n
Example Question #1 : How To Add Exponents
Simplify: 3y2 + 7y2 + 9y3 – y3 + y
19y11
10y4 + 8y6 + y
10y2 + 10y3 + y
10y2 + 9y3
10y2 + 8y3 + y
10y2 + 8y3 + y
Add the coefficients of similar variables (y, y2, 9y3)
3y2 + 7y2 + 9y3 – y3 + y =
(3 + 7)y2 + (9 – 1)y3 + y =
10y2 + 8y3 + y
Example Question #2 : How To Add Exponents
Simplify the following:
When common variables have exponents that are multiplied, their exponents are added. So K3 * K4 =K(3+4) = K7. And M6 * M2 = M(6+2) = M8. So the answer is K7/M8.
Example Question #3 : How To Add Exponents
Solve for 
First, reduce all values to a common base using properties of exponents.
Plugging back into the equation-
Using the formula
We can reduce our equation to
So,
Example Question #41 : Exponents
Simplify: y3x4(yx3 + y2x2 + y15 + x22)
y3x12 + y6x8 + y45x4 + y3x88
y4x7 + y5x6 + y18x4 + y3x26
2x4y4 + 7y15 + 7x22
y3x12 + y6x8 + y45 + x88
y3x12 + y12x8 + y24x4 + y3x23
y4x7 + y5x6 + y18x4 + y3x26
When you multiply exponents, you add the common bases:
y4 x7 + y5x6 + y18x4 + y3x26
Example Question #5 : Exponential Operations
If 
Rewrite the term on the left as a product. Remember that negative exponents shift their position in a fraction (denominator to numerator).
The term on the right can be rewritten, as 27 is equal to 3 to the third power.
Exponent rules dictate that multiplying terms allows us to add their exponents, while one term raised to another allows us to multiply exponents.
We now know that the exponents must be equal, and can solve for 
Example Question #83 : Exponential Operations
If 
Since the base is 5 for each term, we can say 2 + n =12. Solve the equation for n by subtracting 2 from both sides to get n = 10.
Example Question #2233 : Act Math
Which expression is equivalent to the following?
None of these
None of these
The rule for adding exponents is 
You could combine the first two terms into 
Example Question #2234 : Act Math
Express as a power of 2:
The expression cannot be rephrased as a power of 2.
Since the problem requires us to finish in a power of 2, it's easiest to begin by reducing all terms to powers of 2. Fortunately, we do not need to use logarithms to do so here.
Thus,
Example Question #42 : Exponents
Simplify the following expression:
When multiplying bases that have exponents, simply add the exponents. Note that you can only add the exponents if the bases are the same. Thus:
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