Exponents

Multiplication

100

(-2y⁶z¹⁴)(7y³z)

-14y⁹z¹⁵

200

(-3j⁴k¹⁷)²

9j⁸k³⁴

300

[(2²)²]²

256

400

Cleavon has money in an account that earns 4% simple interest. The formula for computing simple interest is I=Prt, where I is the interest earned, P is the principal amount he put into the account, r is the interest rate, and t represents time in years.

What is the interest earned if he makes a deposit of 3b and leaves it for b years?

I = 0.12b²

500

A cylinder has a radius of 2x meters and a height of 3x² meters. What is the surface area of the cylinder? (you may write only pi or use 3.14)

Division

100

m⁴p³ / 3m²n⁴p⁴

m² / 3n⁴p

200

r³st^-4 / s⁵t

r³ / s⁴t⁵

300

g⁰h⁷j^-4 / g^-2h^-1j^-4

g²h⁸

400

The probability of rolling a die and getting an even number is 1/2. If you roll the die twice, the probability is (1/2)². What is the probability of getting an even number 5 times? 

(1/2)⁵ = 1/32

500

The processing speed of an older desktop computer is about 10⁸ instructions per second. A newer computer can process about 10¹³ instructions per second. How many times is the old computer as fast as the newer one?

10⁸ / 10¹³ = 1 / 100000

Rational Exponents

100

Write xy^1/2 in radical form

x squareroot(y)

200

Write x^1/3y^2/3z^0/3 in radical form.

cuberoot(xy²)

300

Write the phrase "2 times the fourth root of k raised to 7" into exponent form

2k^7/4

400

The frequency f in hertz of the nth key on a piano is f = 440(2^1/12)^n-49

What is the frequency at the 52nd key on a piano?

440 fourth root(2)

500

The frequency f in hertz of the nth key on a piano is f = 440(2^1/12)^n-49

Which note has a frequency of 110 hertz (Hz)?

25th note

I didn't do my homework

100

Simplify: squareroot of (24x⁶y⁹)

2x³y⁴ squareroot of (6y)

200

Simplify -10(squareroot of 3) + 7(squareroot of 3)

-3(squareroot of 3)

300

Simplify 4 / (2 + squareroot of 5)

-8 + 4 (squareroot of 5)

400

Simplify: Squareroot of 8 + squareroot of 12 + squareroot of 18

5(squareroot of 2) + 2(squareroot of 3)

500

The area A of a triangle can be found using the formula A = 1/2 bh.

What is the area of a triangle with:

height  = four(squareroot of 5) - 2(squareroot of 2) cm

base = squareroot of 2 + 2(squareroot of 5) cm

18cm²