Index laws

Simple index laws

100

y⁸*y^-2

y⁶

200

(p⁵)²

p¹⁰

300

(p^-2)^-1

p²

400

(q²)³*(q⁵/q)²

q¹⁴

500

x*(x*(x³)²)²

x¹⁵

Zero and negative indices

100

6^-1

1/6

200

9⁰

1

300

8^-2

1/64

400

(8/9)^-2

81/64

500

2^y=1/4

y=?

y=-2

Indices to products

100

(2cd⁴)³

8c³d¹²

200

(9a²)²

81a⁴

300

(16a⁴b³)^-2

1/256a^-8b^-6

400

(xy²)²/3x²

y⁴/3

500

(18a³b²)/6(a²b⁵)^-1

3a⁵b⁷

Write as a power of...

100

Write as a single power of 2:

4¹⁰

2²⁰

200

Write as a signle power of 2:

8^x*2⁴=

2^3x+4

300

Write as a signle power of 2:

2^x *4^y*16=

2^x+2y+4

400

Solve for x:

8^x=2⁹

x=3

500

Solve for x:

4^x=8⁶/2⁴

x=7

Extra hard questions (double points)

100

Simplify:

2^2y+2^2y

2^2y+1

200

Solve:

(2^x)⁵/2³=2/(2⁴)^x

x=4/9

300

100^a*1000^b can be written in the form of 10^w.

Express w in terms of a and b

w=2a+3b

400

Let x=2^p, y=2^q

If xy=32 and 2xy²=32, find the values of p and q

p=6

q=-1

500

You are given that x=5^m and y=5ⁿ

a) Write 5^m+2 in terms of x

b)Write 5^m-n in terms of x and y

a)25x

b)x/y