GRE Quantitative Reasoning - How to divide exponents

If , then $\frac{(c^3)^2}{c^2c^4}=?$

Cannot be determined

Explanation

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.

Simplify

$\dpi{100} \small \frac{20x^{4}y^{-3}z^{2}}{5z^{-1}y^{2}x^{2}}=$

$\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}$

$\dpi{100} \small {4x^{5}y^{-2}}$

$\dpi{100} \small 15x^{2}y^{2}z^{2}$

$\dpi{100} \small 15x^{-2}y^{-2}z^{-2}$

None

Explanation

Divide the coefficients and subtract the exponents.

Evaluate:

$\frac{(2x^3y^{-2}a^6z^4)^5}{(4xy^4a^{-3}z^4)^2}$

$\frac{5x^{13}y-2az^{12}}{4}$

$\frac{5x^{13}y-2az^{12}}{4y}$

$\frac{2x^{13}a^{36}z^{12}}{y^{18}}$

$2x^{13}-18a-36z^{12}$

$\frac{2x^{13}z^{12}}{y^{18}a^{36}}$

Explanation

Distribute the outside exponents first:

$\frac{2^5x^{15}y^{-10}a^{30}z^{20}}{4^2x^2y^8a^{-6}z^8}$

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

$\frac{2x^{13}a^{36}z^{12}}{y^{18}}$

Which of the following is equal to the expression Equationgre , where

xyz ≠ 0?

1/y

xyz

z/(xy)

Explanation

(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.

If $a ot\equiv0$ , which of the following is equal to $\frac{(a^6*a^2)^3}{a^6}$ ?

a18

The answer cannot be determined from the above information

Explanation

The numerator is simplified to (by adding the exponents), then cube the result. a24/a6 can then be simplified to $a^{18}$ .

$\dpi{100} \small \frac{7^{10}-7^{8}}{7^{9}-7^{7}}=$

$\dpi{100} \small 7$

$\dpi{100} \small 42$

$\dpi{100} \small 49$

$\dpi{100} \small 28$

$\dpi{100} \small 343$

Explanation

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 .

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}$

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

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}=\frac{7^3-7^1}{7^2-1}=\frac{343-7}{49-1}=\frac{336}{48}=7$

\[641/2 + (–8)1/3\] * \[43/16 – 3171/3169\] =

–30

–5

Explanation

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.

How to divide exponents

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