ACT Math : How to subtract exponents

Example Questions

Example Question #1 : How To Subtract Exponents

Reduce  to simplest form.

Explanation:

When dividing terms with the same bases but different exponents, you will need to subtract all the pertinent exponents.

becomes ,

becomes ,

and  stays the same because there is no other z term to combine with it.

Thus resulting in:

Example Question #1 : How To Subtract Exponents

Simplify: 32 * (423 - 421)

4^4

3^3 * 4^21 * 5

3^3 * 4^21

3^21

3^3 * 4^21 * 5

Explanation:

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 #1 : How To Subtract Exponents

Simplify. Leave no negative exponents in the final answer.

None of these are the correct answer.

Explanation:

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

Thus,

Example Question #1 : How To Subtract Exponents

Simplify to remove fractions:

None of these are correct.

Explanation:

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.

So,

Example Question #5 : How To Subtract Exponents

Simplify the following:

Explanation:

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 #1 : How To Subtract Exponents

can be written as which of the following?

A.

B.

C.

B only

A, B and C

B and C

A and C

C only

B and C

Explanation:

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 #1 : How To Subtract Exponents

Simplify:

Explanation:

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.