Multiplying and Dividing Exponents - Algebra 2

Put the negative exponent on the bottom so that you have which simplifies further to .

To simplify variables with exponents through division, you must subtract the exponent in the denominator from the numerator.

Remember that negative exponents will eventually be moved back to the denominator.

Rewrite so that you are multiplying the reciprocal of the second fraction:

You can then simplify using rules of exponents:

Rearrange the expression so that the and variables of different powers are right next to each other.

When multiplying the same variable with different exponents, it is the same as adding the exponents: . Taking advantage of this rule, the problem can be rewritten.

In this problem, you have two fractions being multiplied. You can first divide and cancel the coefficients in the numerators and denominators, by dividing 9 and 3 each by 3:

Next you can multiply the two numerators, and multiply the two denominators. Remember that when multiplying like variables with exponents, you add the exponents together:

If a variable shows up in both the numerator and denominator, you can simplify by subtracting the numerator's exponent by the denominator's exponent. If you end up with a negative exponent in the numerator, you can move the variable and exponent to the denominator to make it positive:

In this problem, you have two fractions being multiplied. You can first divide and cancel the coefficients in the numerators and denominators, by dividing 10 and 5 each by 5 and dividing 21 and 7 each by 7:

Next you can multiply the two numerators, and multiply the two denominators. Remember that when multiplying like variables with exponents, you add the exponents together:

If a variable shows up in both the numerator and denominator, you can simplify by subtracting the numerator's exponent by the denominator's exponent:

In this problem, you have two fractions being multiplied. You can first divide and cancel the coefficients in the numerators and denominators. The two coefficients in the denominators multiply up to 15, allowing you to divide and cancel those two coefficients with the 15 in the numerator:

Next you can multiply the two numerators, and multiply the two denominators. Remember that when multiplying like variables with exponents, you add the exponents together:

If a variable shows up in both the numerator and denominator, you can simplify by subtracting the numerator's exponent by the denominator's exponent. If you end up with a negative exponent in the numerator, you can move the variable and exponent to the denominator to make it positive:

Combine like terms in the numerator and the denominator. Use the rules of exponents to combine and in the numerator and and in the denominator. Remember that Then, divide 30 by 5 (the GCF).

The GCF rule can also be used to remove from the numerator and the deonominator. goes into once.

We can also solve this problem using a different apporach

Remember that any number raised to the 0th power equals 1

Alternatively,

Alternatively,

Remember that any number raised to the 0th power equals 1

Step 1: Simplify the exponents using the division of exponents rule (subtract exponents in demoninator from exponents in numerator).

Step 2: Reduce the fraction

Follow the division of exponents rule. Subract the exponents in the denominator from the exponents in the numerator.

Based on the property for dividing exponents:

In this problem, a is equal to , so

Simplify:

Step 1: Use the division of exponents rule, and subtract the exponents in the denominator from the exponents in the numerator

Step 2: Move negative exponents in the numerator to the denominator

Step 3: Simplify

Step 1: Use the division of exponents rule. Subtract the exponents in the numerator from the exponents in the denominator.

Step 2: Represent the negative exponents as positive ones by moving them to the denominator:

When dividing variables with exponents, you subtract the denominator exponents from the numerator exponents of the corresponding variable:

, then simplify: .

In order to remove the negative exponent, we move it to the denominator.

Therefore, the answer is .

When multiplying variables with the same base, you add the exponents. So, .