Free Printable PROPERTIES OF EXPONENTS and SCIENTIFIC NOTATION

1.

Simplify the expression. Use only positive exponents. $\frac{a^5b^9c^{-3}}{a^8b^{-2}c^7}$

a)

$\frac{b^{11}}{a^3c^{10}}$

b)

$\frac{a^3b^{11}}{c^{10}}$

c)

$\frac{c^{10}}{a^3b^{11}}$

d)

$a^3b^{11}c^{10}$

2.

Simplify the expression. Use only positive exponents $\left(\frac{x^6y^9z^{-5}}{x^{10}y^{-3}z^2}\right)^{-4}$

a)

$\frac{x^{16}y^{48}}{z^{28}}$

b)

$x^{28}y^{16}z^{48}$

c)

$\frac{y^{48}z^{28}}{x^{16}}$

d)

$\frac{x^{16}z^{28}}{y^{48}}$

3.

Simplify the expression. Use only positive exponents $\left(\frac{2x^2}{3y^2}\right)^0$

a)

1

b)

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

c)

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

4.

Simplify the expression. Use only positive exponents $\left(3x^2y^5\right)^3\cdot\left(5x^{-2}y^2\right)^{-2}$

a)

$\frac{25x^{10}}{27y^{11}}$

b)

$\frac{27}{25x^{10}y^{11}}$

c)

$\frac{27x^{10}y^{11}}{25}$

d)

$\frac{25x^{10}y^{11}}{27}$

5.

Simplify the expression. Use only positive exponents $\left(\frac{2x^{-4}y^2z^3}{3xy^3z^{-2}}\right)^{-2}$

a)

$\frac{4x^{10}z^{10}}{9y^2}$

b)

$\frac{9x^{10}y^2z^{10}}{4}$

c)

$\frac{9x^{10}y^2}{4z^{10}}$

6.

Simplify the expression shown. Your answer should contain only positive exponents.

a)

b)

c)

d)

7.

Simplify the expression shown. Your answer should contain only positive exponents.

a)

b)

c)

d)

8.

Simplify the expression shown. Your answer should contain only positive exponents.

a)

4x⁶

b)

y⁴

c)

32x⁵y⁴

d)

-4x⁷y³

9.

Simplify the expression shown. Your answer should contain only positive exponents.

a)

b)

c)

d)

10.

Simplify the expression shown. Your answer should contain only positive exponents.

a)

3x²y⁴

b)

-3xy⁴

c)

1/3x³y⁴

d)

x²y⁴/3

11.

A sample of bacteria triples each months. The expression

5400\cdot3^m

models a population of 5400 bacteria after m months of growth. Evaluate the expression for m= -2 and m= 2. Describe what each value of the expression represents in the situation.

a)

For m= -2, the population is 600, 2 months before the population is 5400. For m= 2, the population is 48600, 2 months after the population is 5400.

b)

For m= -2, the population is 600, 2 months after the population is 5400. For m= 2, the population is 48600, 2 months before the population is 5400.

c)

For m= -2, the population is -600, 2 months before the population is 5400. For m= 2, the population is 58600, 2 months after the population is 5400.

d)

For m= -2, the population is 700, 2 months after the population is 5400. For m= 2, the population is 58600, 2 months before the population is 5400.

12.

A human body contains about

3.2\ \cdot10^4\ \mu L\ \left(microliters\right)\

of blood for each pound of body weight. Each microliter of blood contains about

5\cdot10^6

red blood cells. Find the approximate number of red blood cells in the body of a 125-lb person.

a)

$There\ are\ about\ 2\cdot10^{12}\ red\ blood\ cells.$

b)

$There\ are\ about\ 2\cdot10^{14}\ red\ blood\ cells.$

c)

$There\ are\ about\ 2\cdot10^{13}\ red\ blood\ cells.$

d)

$There\ are\ about\ 2\cdot10^{-13}\ red\ blood\ cells.$

13.

There are about $3.35\cdot10^{25}$ molecules in a liter of water. Pine Lake. in New York, has about $2\cdot10^8$ liters of water. About how many molecules of water are in Pine Lake?

a)

$About\ 67\cdot10^{32\ }\ molecules.$

b)

$About\ 6.7\cdot10^{32\ }\ molecules.$

c)

$About\ 6.69\cdot10^{34\ }\ molecules.$

d)

$About\ 6.7\cdot10^{33\ }\ molecules.$

14.

The term mole can be used in chemistry to refer to

6.02\times10^{23}\ atoms\

of a substance. The mass of a single hydrogen atom is approximately

1.67\times10^{-24}\ gram.\

What is the mass of 1 mole of hydrogen atoms?

a)

About 1.01 g

b)

About 10.1 g

c)

About 0.101 g

d)

About 1.1 g

15.

$1.45\cdot10^{-1}\ kWh\ \left(kilowatt-hour\right)$ is what an hour of television use consumes of electricity. Each kilowatt-hour of electric use is equivalent to $3.6\cdot10^6\ joules\ of\ energy.$ Find how many joules a television uses in 1 hour.

a)

$4.22\cdot10^5\ joules$

b)

$5.22\cdot10^5\ joules$

c)

$5.22\cdot10^4\ joules$

d)

$4.22\cdot10^4\ joules$

16.

Simplify the quotient. Write the answer in scientific notation.

\frac{8.4\cdot10^{-5}}{2\cdot10^{-8}}

a)

$4.5\cdot10^4$

b)

$4.2\cdot10^3$

c)

$5.4\cdot10^3$

d)

$4.1\cdot10^4$

17.

In 1990, the United States government owed

3.23\cdot10^{12}

dollars to its creditors. The population of the United States was

2.487\cdot10^8

people. How much did the government owe per person in 1990? Round to the nearest dollar.

a)

About $12,900

b)

About $13,900

c)

About $12,900

d)

About $12,988

18.

One pint of blood contains about $2.4\cdot10^{12}\$ red blood cells. Your body normally produces about $2\cdot10^6$ red blood cells per second. If you donate blood, In how many seconds will your body replace the red blood cells lost by giving one pint of blood?

a)

$About\ 1.5\cdot10^6\ s.$

b)

$About\ 1.2\cdot10^6\ s.$

c)

$About\ 1.2\cdot10^5\ s.$

d)

$About\ 1.5\cdot10^5\ s.$

PROPERTIES OF EXPONENTS and SCIENTIFIC NOTATION

Total questions: 18

Worksheet time: 5hrs 30mins

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