ACT Math : Exponential Operations
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Example Questions
Example Question #31 : Exponential Operations
Simplify:
When an exponent is raised to an exponent, multiply the two together to yield a new exponent, and attach that exponent to the original base.
In this case, multiply 
Example Question #32 : How To Multiply Exponents
Solve: 
When an exponent is raised to another exponent, you may multiply them together to find the exponent of the answer. Attach that exponent to the original base, and that is the solution.
In this particular problem, multiply 
Now, substitute 
Example Question #32 : Exponential Operations
What is
Negative exponents are reciprocals. Do not change the sign to negative.
The variables with negative exponents can be written as their reciprocals.
Multiplying these new forms together gives,
From here, simplify by factoring out a common factor from the numerator and denominator.
Example Question #731 : Algebra
Simplify the following:
To solve, simply distribute the outer exponent. When you have an exponent to an exponent, you multiply their values. Thus,
Example Question #33 : Exponential Operations
Which of the following is a value of x that satisfies
3
0
4
2
1
2
This question incorporates properties of exponents. The best way to solve this problem is to establish the same base for all of the terms.
Now use the properties of exponents to simplify the left side of the equation. When exponential terms with the same base are multiplied, the exponents are added.
Now, with the left side simplified, set that equal to 
Since each side has one term with the same base, simply set the exponents equal to each other and solve for x.
Example Question #1 : How To Add Exponents
For all x, 2x2 times 12x3 equals...
0
24x6
24x5
14x5
14x6
24x5
You multiply the integers, then add the exponents on the x's, giving you 24x5.
Example Question #34 : Exponential Operations
Multiply: 2x² * 3x
5x3
6x3
2x3
5x
6x²
6x3
When multiplying exponents you smiply add the exponents.
For 2x² times 3x, 2 times 3 is 6, and 2 + 1 is 3, so 2x² times 3x = 6x3
Example Question #3 : How To Add Exponents
What is 23 + 22 ?
64
32
20
12
12
Using the rules of exponents, 23 + 22 = 8 + 4 = 12
Example Question #35 : Exponential Operations
Solve for 
2
3
5
1
9
1
The only value of x where the two equations equal each other is 1. All you have to do is substitute the answer choices in for x.
Example Question #5 : How To Add Exponents
A particle travels 9 x 107 meters per second in a straight line for 12 x 10-6 seconds. How many meters has it traveled?
1.08 x 103
1.08
1.08 x 10
1.08 x 105
1.08 x 103
Multiplying the two numbers yields 1080. Expressed in scientific notation 1080 is 1.08 x 103.
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