All ACT Math Resources
Example Question #1 : How To Subtract Exponents
Reduce to simplest form.
When dividing terms with the same bases but different exponents, you will need to subtract all the pertinent exponents.
and stays the same because there is no other z term to combine with it.
Thus resulting in:
Example Question #52 : Exponents
Simplify: 32 * (423 - 421)
None of the other answers
3^3 * 4^21
3^3 * 4^21 * 5
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 and :
Lastly, simplify the negative exponent using
Example Question #3 : 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 , to get:
Next, combine using multiplication and the rule :
Since the problem specifies that we must avoid fractions, we will not eliminate the negative exponents.
Example Question #4 : How To Subtract Exponents
Simplify the following:
When dividing exponential expressions with the same base, subtract the exponents. In this problem, the exponents are and . When subtracted, the result is . Thus, the correct answer is .
Example Question #5 : How To Subtract Exponents
can be written as which of the following?
A and C
B and C
A, 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 instead of .
B is equivalent by the aforementioned exponential property, while C is simply computing the expression.
Example Question #6 : How To Subtract Exponents
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 from . That yields as the new exponent and as the answer.