ACT Math : Exponential Operations
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Example Questions
Example Question #6 :How To Add Exponents
Simplify: hn+ h–2n
h–2n= 1/h2n
hn+ h–2n= hn+ 1/h2n
Example Question #7 :How To Add Exponents
Simplify: 3y2+ 7y2+ 9y3.– y3.+ y
10 y2+ 10y3.+ y
19y11
10 y2+ 9y3.
10 y4+ 8y6+ y
10 y2+ 8y3.+ y
10 y2+ 8y3.+ y
Add the coefficients of similar variables (y, y2, 9y3.)
3.y2+ 7y2+ 9y3.– y3.+ y =
(3 + 7)y2+ (9 – 1)y3.+ y =
10 y2+ 8y3.+ y
Example Question #8 :How To Add Exponents
Simplify the following:
When common variables have exponents that are multiplied, their exponents are added. SoK3.*K4=K(3.+4)=K7. AndM6*M2=M(6+2)=M8. So the answer isK7/M8.
Example Question #9 :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 #4 :Exponential Operations
Simplify: y3.x4(yx3.+ y2x2+ y15+ x22)
y3.x12+ y6x8+ y45x4+ y3.x88
y4x7+ y5x6+ y18x4+ y3.x26
y3.x12+ y6x8+ y45+ x88
y3.x12+ y12x8+ y24x4+ y3.x23
2x4y4+ 7y15+ 7x22
y4x7+ y5x6+ y18x4+ y3.x26
When you multiply exponents, you add the common bases:
y4x7+ y5x6+ y18x4+ y3.x26
Example Question #6 :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 #11 :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 #41 :Exponents
Which expression is equivalent to the following?
None of these
None of these
The rule for adding exponents is
Youcouldcombine the first two terms into
Example Question #42 :Exponents
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 #43 :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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