NEGATIVE INDEX LAW WORKSHEET

Simplify the following and give answer in simplest rational form :

Problem 1 :

4^-1

Solution

Problem 2 :

9^-2

Solution

Problem 3 :

3^-3

Solution

Problem 4 :

10^-5

Solution

Problem 5 :

(1/2)^-1

Solution

Problem 6 :

(2/3)^-2

Solution

Problem 7 :

(1  3/4)^-2

Solution

Problem 8 :

2⁰ + 2^-1

Solution

Problem 9 :

3⁰ + 3¹ - 3^-1

Solution

Problem 10 :

2a^-1

Solution

Problem 11 :

(5c)^-2

Solution

Problem 12 :

2(ab)^-1

Solution

Problem 13 :

2ab^-1

Solution

Problem 14 :

(3n^-2)^-1

Solution

Write each of the followings as fractions

Problem 15 :

8^-2/3

Solution

Problem 16 :

25^-3/2

Solution

Problem 17 :

Arrange in order from smallest to largest

1/50, 5^-2, 3/10, 2^-3

Solution

Problem 18 :

Simplify : 2^-2 + 3^-2 x 2^-3

Solution

Problem 19 :

Given that 

2^m + 2ⁿ = 9/32

Work out mn

Solution

Problem 20 :

Put the expressions above in order, from smallest to largest,

when: x = 2 and x = 0.5

x^-2, x⁰, x, x³

Solution

Problem 21 :

What is the value of the missing exponent in the equation (3x^?y⁴)^-3 = x⁶/27y¹² ?

a) 2    b)  -2   c)  3   d) -3

Solution

Problem 22 :

Which expression is equivalent to (-3 • 6⁰ • 4)^-2 ?

a) -144    b)  144   c)  1/144   d) -1/144

Solution

Evaluate the following without using calculator.

Problem 1 :

5^-2                   Solution

Problem 2 :

25^-1/2                  Solution

Problem 3 :

(16/25)^-3/2                Solution

Problem 4 :

(4y)^-2             Solution

Problem 5 :

(27b)^1/3 / (9b)^-1/2             Solution

Problem 6 :

b^-1/2 = 4, what is the value of b ?              Solution

Problem 7 :

(2^m)^-6 = 16, what is the value of 2³ x m ?       Solution

Problem 8 :

If 4ⁿ = 20, then what is the value of 4^-n ?         Solution

Problem 9 :

If a^-1/2 = 3, what is the value of a ?       Solution

Problem 10 :

If 3^x = 10, what is the value of 3^x-3 ?        Solution

Problem 11 :

A drop of water leaks from a faucet every second. How many liters of water leak from the faucet in 1 hour?

Solution

Example 12 :

a)  If a is a nonzero number, does the value of a⁰ depend on the value of a?

b)  Explain how to evaluate 10⁻³

c)  Without evaluating, order 5⁰, 5⁴, and 5⁻⁵ from least to greatest.

Solution

Example 13 :

Which is different? Find “both” answers.

a)  Rewrite 1/(3 ⋅ 3 ⋅ 3)   using a negative exponent.

b)  Write 3 to the negative third power.

c)  Write 1/3 cubed as a power.

d)  Write (−3) ⋅ (−3) ⋅ (−3) as a power.

Solution

Example 14 :

Use the Quotient of Powers Property to copy and complete the table.

a) What patterns do you see?

b)  How would you define 5⁰? Why?

c) How can you rewrite 5⁻¹ as a fraction?

Solution

Example 15 :

Describe and correct the error in evaluating the expression.

Solution

Write the expression with only positive exponents. Assume all variables represent non zero numbers. Simplify if necessary.

Problem 1 : 

4r³(r⁴)³ / 15(r³)^-2

(a) 4/15r²¹  (b)  4r²¹/15  (c)  4r⁹/15  (d)  4/15r⁹

Solution

Problem 2 : 

(-4x⁴y^-5)³ (2x^-1y)

(a) -8x⁵/y⁶  (b)  -2x³/y⁴  (c)  -8x^-3/y⁴  (d)  -8x³y⁶

Solution

Problem 3 : 

[(12x^-5y^-3 z⁴) / (3xy^-3z^-4)]^-1

(a) x⁴/4z⁸  (b)  x⁶/4z⁸  (c)  4x⁶/z⁸  (d)  x⁶y⁶/4z⁸

Solution

Problem 4 : 

[(xy⁵) / (x³y)]^-2

(a) 1/x⁸ y¹²  (b)  x⁴/y⁸  (c)  1/x⁵y¹¹  (d)  y⁸/x⁴

Solution

Problem 5 :

Which is the simplified form of (3a²b³c^-2)/(a^-1b²c)³ ?

(a) 3a⁵/b³c⁵  (b)  3ab/c⁵  (c) 3/b²c⁵  (d) 3/ab³c⁵

Solution

Problem 5 :

A jelly fish emits about 1.25 × 10⁸ particles of light, or photons, in 6.25 × 10⁻⁴ second. How many photons does the jelly fish emit each second? Write your answer in scientific notation and in standard form.

Solution

Problem 6 :

A microscope magnifies an object 10⁵ times. The length of an object is 10⁻⁷ meter. What is its magnified length?

Solution

Problem 7 :

Simplify the expression. Write your answer using only positive exponents.

a)  x^-7

b)  y⁰

c)  9x⁰ y^-3

d)  15c^-8 d⁰

e)  (2^-2 m^-3)/n⁰

f)  (10⁰ r^-11s)/3²

g)  (4^-3 a⁰)/b^-7

h)  p^-8 / 7^-2 q^-9

i)  (2² y^-6)/8^-1 z⁰ x^-7

Solution

Problem 8 :

The mass of a grain of sand is about 10^-3  gram. About how many grains of sand are in the bag of sand?

Problem 9 :

Evaluate and order 5⁰, 5⁴, and 5^-5 from least to greatest

Solution

Problem 10 :

A drop of water leaks from a faucet every second. How many liters of water leak from the faucet in 1 hour?

Solution