ACT Math - How to divide exponents

What is the value of m where:

$64^{\frac{n}{12}}=(m)4^{(\frac{1+m}{m+n})}$

-2

Explanation

If n=4, then 64(4/12)=64(1/3)=4. Then, 4=m4(1+m)/(m+4). If 2 is substituted for m, then 4=24(1+2)/(2+4)=241/2=2√4=22=4.

$64^{\frac{4}{3}}$ can be written as which of the following?

A. $\sqrt[3]{64^4}$

B. $(\sqrt[3]{64})^{4}$

A, B and C

B and C

A and C

C only

B only

Explanation

C is computing the exponent, while A and B are equivalent due to properties of fractional exponents.

Remember that...

$a^{\frac{b}{c}} = \sqrt[c]{a^b} = (\sqrt[c]{a})^b$

$64^{\frac{4}{3}}=$ $\sqrt[3]{64^4}=$ $(\sqrt[3]{64})^{4}=$

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.

Simplify Actmath_45_508_q9

Actmath_45_508_q9_3

Actmath_45_508_q9_4

Actmath_45_508_q9_2

Actmath_45_508_q9_5

None of the answers are correct

Explanation

When working with polynomials, dividing is the same as multiplying by the reciprocal. After multiplying, simplify. The correct answer for division is

Actmath_45_508_q9_2

and the correct answer for multiplication is

Actmath_45_508_q9_3

Simplify:

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

$\small \frac{z^2}{xy}$

$\small xyz^2$

$\small \frac{z}{x^2y^2}$

$\small \frac{yz^2}{x}$

Explanation

To simply exponents in a fraction, subtract the exponent for each variable in the denominator from the exponent in the numerator. This will leave you with

$\small x^{-1}y^{-1}z^2$ or $\small \frac{z^2}{xy}$

Simplify:

$\frac{x^{4}}{x^{3}}$

$x^{\frac{4}{3}}$

$x^{2}$

Explanation

When exponents with the same base are being divided, you may substract the exponent in the denominator from the exponent in the numerator to create a new exponent. In this case, you would subtract from , yielding as the new exponent. Keeping the same base, the answer becomes .

Simplify:

$\left (\frac{18a^3b^3}{3a^{-1}b^{-2}} \right )^2$

$36a^8b^{10}$

Explanation

Simplify:

$\left (\frac{18a^3b^3}{3a^{-1}b^{-2}} \right )^2$

Step 1: Simplify the fraction. When dividing exponents subtract the exponents on the bottom from the exponents on the top.

$\left (\frac{18a^3b^3}{3a^{-1}b^{-2}} \right )^2 =\left ( 6a^4b^5 \right )^2$

Step 2: Distribute the exponent. When raising an exponent to a power, multiply them together.

$(6a^4b^5)^2 = 36a^8b^{10}$

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.

Simplify the following

$\frac{4x^5y^-^4z^4}{2x^-^2y^-^2z^5}$ .

$\frac{2x^7}{y^2z}$

$\frac{2x^3y^3}{z}$

$\frac{32x^2y}{z}$

$\frac{y^3z^2}{64x^3}$

$\frac{x^3}{16y^3z}$

Explanation

Start by remembering that you "flip" negative exponents over the division bar, thus moving from the top to the bottom and vice-versa. (There are other ways to do this as well, though most students understand this way most easily.)

$\frac{4x^5x^2y^2z^4}{2y^4z^5}$