ACT Math : Algebra
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Example Questions
Example Question #42 : 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 #43 : 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 #1 : How To Add Exponents
Simplify: y3x4(yx3 + y2x2 + y15 + x22)
y4x7 + y5x6 + y18x4 + y3x26
y3x12 + y6x8 + y45 + x88
y3x12 + y6x8 + y45x4 + y3x88
y3x12 + y12x8 + y24x4 + y3x23
2x4y4 + 7y15 + 7x22
y4x7 + y5x6 + y18x4 + y3x26
When you multiply exponents, you add the common bases:
y4 x7 + y5x6 + y18x4 + y3x26
Example Question #741 : Algebra
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 #742 : Algebra
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 #44 : 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:
Example Question #743 : Algebra
Simplify the following:
When multiplying two exponential expressions with the same bases, add the exponents. In this problem, the answer turns out to be 
Example Question #2241 : Act Math
Simplify the following
Begin by performing the last group's multiplication:
Now, remember that you treat variables and their powers as similar terms to be combined. Therefore, you can combine the 
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