ACT Math : Exponential Operations
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Example Questions
Example Question #11 : How To Add Exponents
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 
Example Question #1 : How To Subtract Exponents
Reduce 
When dividing terms with the same bases but different exponents, you will need to subtract all the pertinent exponents.
and 
Thus resulting in:
Example Question #1 : How To Subtract Exponents
Simplify: 32 * (423 - 421)
4^4
None of the other answers
3^3 * 4^21 * 5
3^21
3^3 * 4^21
3^3 * 4^21 * 5
Begin by noting that the group (423 - 421) has a common factor, namely 421. You can treat this like any other constant or variable and factor it out. That would give you: 421(42 - 1). Therefore, we know that:
32 * (423 - 421) = 32 * 421(42 - 1)
Now, 42 - 1 = 16 - 1 = 15 = 5 * 3. Replace that in the original:
32 * 421(42 - 1) = 32 * 421(3 * 5)
Combining multiples withe same base, you get:
33 * 421 * 5
Example Question #2 : How To Subtract Exponents
Simplify. Leave no negative exponents in the final answer.
None of these are the correct answer.
The first step in the problem is to combine like terms in the numerator, remembering that 
Next, we resolve the numerator, using 
Lastly, simplify the negative exponent using
Thus,
Example Question #1 : How To Subtract Exponents
Simplify to remove fractions:
None of these are correct.
The first step is to simplify each fraction by dividing like terms, remembering that 
Next, combine using multiplication and the rule 
Since the problem specifies that we must avoid fractions, we will not eliminate the negative exponents.
So,
Example Question #2 : How To Subtract Exponents
Simplify the following:
When dividing exponential expressions with the same base, subtract the exponents. In this problem, the exponents are 
Example Question #1 : How To Subtract Exponents
A.
B.
C.
A and C
A, B and C
C only
B only
B and C
B and C
A is not equivalent because exponents in denominators mean subtraction of exponents and not division of them. Furthermore, A, when computed, comes out to 
B is equivalent by the aforementioned exponential property, while C is simply computing the expression.
Example Question #1 : How To Subtract Exponents
Simplify:
When two exponents with the same base are being divided, subtract the exponent of the denominator from the exponent of the numerator to yield a new exponent. Attach that exponent to the base, and that is your answer.
In this case, subtract 
Example Question #1 : How To Divide Exponents
Simplify 
None of the answers are correct
When working with polynomials, dividing is the same as multiplying by the reciprocal. After multiplying, simplify. The correct answer for division is
and the correct answer for multiplication is
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