How to divide exponents - GRE Quantitative Reasoning

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

Distribute the outside exponents first:

Divide the coefficient by subtracting the denominator exponents from the corresponding numerator exponents:

The numerator is simplified to (by adding the exponents), then cube the result. a24/a6 can then be simplified to .

Let's look at the two parts of the multiplication separately. Remember that (–8)1/3 will be negative. Then 641/2 + (–8)1/3 = 8 – 2 = 6.

For the second part, we can cancel some exponents to make this much easier. 43/16 = 43/42 = 4. Similarly, 3171/3169 = 3171–169 = 32 = 9. So 43/16 – 3171/3169 = 4 – 9 = –5.

Together, \[641/2 + (–8)1/3\] * \[43/16 – 3171/3169\] = 6 * (–5) = –30.

Divide the coefficients and subtract the exponents.

The easiest way to solve this is to simplify the fraction as much as possible. We can do this by factoring out the greatest common factor of the numerator and the denominator. In this case, the GCF is .

Now, we can cancel out the from the numerator and denominator and continue simplifying the expression.

(xy)4 can be rewritten as x4y4 and z0 = 1 because a number to the zero power equals 1. After simplifying, you get 1/y.

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

Distribute the outside exponents first:

Divide the coefficient by subtracting the denominator exponents from the corresponding numerator exponents:

The numerator is simplified to (by adding the exponents), then cube the result. a24/a6 can then be simplified to .

Let's look at the two parts of the multiplication separately. Remember that (–8)1/3 will be negative. Then 641/2 + (–8)1/3 = 8 – 2 = 6.

For the second part, we can cancel some exponents to make this much easier. 43/16 = 43/42 = 4. Similarly, 3171/3169 = 3171–169 = 32 = 9. So 43/16 – 3171/3169 = 4 – 9 = –5.

Together, \[641/2 + (–8)1/3\] * \[43/16 – 3171/3169\] = 6 * (–5) = –30.

Divide the coefficients and subtract the exponents.

The easiest way to solve this is to simplify the fraction as much as possible. We can do this by factoring out the greatest common factor of the numerator and the denominator. In this case, the GCF is .

Now, we can cancel out the from the numerator and denominator and continue simplifying the expression.

Divide the coefficients and subtract the exponents.

(xy)4 can be rewritten as x4y4 and z0 = 1 because a number to the zero power equals 1. After simplifying, you get 1/y.

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

Distribute the outside exponents first:

Divide the coefficient by subtracting the denominator exponents from the corresponding numerator exponents:

The numerator is simplified to (by adding the exponents), then cube the result. a24/a6 can then be simplified to .

Let's look at the two parts of the multiplication separately. Remember that (–8)1/3 will be negative. Then 641/2 + (–8)1/3 = 8 – 2 = 6.

For the second part, we can cancel some exponents to make this much easier. 43/16 = 43/42 = 4. Similarly, 3171/3169 = 3171–169 = 32 = 9. So 43/16 – 3171/3169 = 4 – 9 = –5.

Together, \[641/2 + (–8)1/3\] * \[43/16 – 3171/3169\] = 6 * (–5) = –30.