SAT Math - How to divide exponents

$\frac{55^{10}}{121^6} \cdot \frac{11^8}{5^{8}} = ?$

$5^2\cdot11^6$

$605^{4}$

$\frac{5^{18}}{11^4}$

$\frac{5^2}{11^4}$

Explanation

The key to this problem is understanding how exponents divide. When two exponents have the same base, then the exponent on the bottom can simply be subtracted from the exponent on top. I.e.:

$\frac{5^x}{5^y} = 5^{x-y}$

Keeping this in mind, we simply break the problem down into prime factors, multiply out the exponents, and solve.

$\frac{55^{10}}{121^6} \cdot \frac{11^8}{5^8} = \frac{(5\cdot 11)^{10}}{5^8}\cdot \frac{11^8}{(11\cdot11)^6} = 11^{10}\cdot\frac{5^{10}}{5^8} \cdot \frac{11^8}{11^{12}} = 5^2 \cdot \frac{11^{10+8}}{11^{12}} = 5^2\cdot11^6$

Solve:

$\frac{x^{6}}{x^{2}}$

$x^{4}$

$x^{3}$

$x^{8}$

$x^{12}$

Explanation

$\frac{x^{6}}{x^{2}}=x ^{6-2}=x^{4}$

Solve:

$\frac{x^{3}}{x^{5}}$

$\frac{1}{x^{2}}$

$x^{2}$

$\frac{1}{x^{10}}$

$x^{8}$

Explanation

When dividing expressions with the same variable, combine terms by subtracting the exponents, while leaving the variable unchanged. For this problem, we do that by subtracting 3-5, to get a new exponent of -2. However, because the exponent is negative, we can place the new expression in the denominator of the fraction and make the exponent positive:

$\frac{x^{3}}{x^{5}}=^{3-5}=x^{-2}=\frac{1}{x^{2}}$

$\frac{x^a}{x^b}=x^4$

and

what is the value of a?

$\frac{80}{13}$

Explanation

When dividing exponents,

$\frac{x^a}{x^b}=x^{a-b}$ .

Therefore,

$x^{a-b}=x^4$ .

If $x^{a-b}= x^4$ , then .

We can now solve the system of equations and .

If we solve for a in the first equation and plug it into the second equation, we get and find the value of b to be .

If we substitute this value of b into the first equation, we can solve for a and find that .

$\frac{2^9}{2^6}$

$2^{1.5}$

$2^{15}$

$2^{54}$

Explanation

When dividing exponents, we need to make sure we have the same base. In this case we do. Then we just subtract the exponents. The answer is $2^{9-6}=2^3$ .

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.

$\frac{3^{57}}{3^{19}}$

$3^{38}$

$3^{1083}$

$3^{76}$

$3^{24}$

Explanation

When dividing exponents, we need to make sure we have the same base. In this case we do. Then we just subtract the exponents. The answer is $3^{57-19}=3^{38}$ .