Free Printable Exponents & Scientific Notation

1.

Simplify with exponents.

2^5\cdot2^3

a)

$2^8$

b)

$2^{15}$

c)

$4^8$

d)

$4^{15}$

2.

$\frac{5^8}{5^2}$

Simplify with exponents.

a)

$1^6$

b)

$1^4$

c)

$5^4$

d)

$5^6$

3.

Choose all expressions that are equivalent to $4^{-5}$

a)

$-4^5$

b)

$\frac{1}{4^5}$

c)

$\frac{1}{1,024}$

d)

$-1,024$

e)

$\frac{1}{4\cdot4\cdot4\cdot4\cdot4}$

4.

Simplify completely.

$\frac{7^2}{7^6}$

a)

$\frac{1}{2,401}$

b)

$2,401$

c)

$343$

d)

$\frac{1}{343}$

5.

Simplify with positive exponents only.

$4^3\cdot4^{-6}$

a)

$4^3$

b)

$4^9$

c)

$\frac{1}{4^3}$

d)

$\frac{1}{4^9}$

6.

Simplify

\left(3x^3\right)\left(6x^5\right)

a)

$18x^8$

b)

$18x^{15}$

c)

$9x^8$

d)

$9x^{15}$

7.

$\frac{32x^{10}}{4x^4}$

a)

$28x^6$

b)

$28x^{14}$

c)

$8x^6$

d)

$8x^{14}$

8.

Simplify.

\left(6x^5\right)^3

a)

$6x^{15}$

b)

$6x^8$

c)

$216x^8$

d)

$216x^{15}$

9.

Simplify

\frac{18x^2}{3x^6}

a)

$6x^4$

b)

$\frac{6}{x^4}$

c)

$6x^3$

d)

$\frac{6}{x^3}$

10.

Simplify.

\frac{9x^4\cdot4x^8}{6x^2}

a)

$6x^{10}$

b)

$6x^6$

c)

$6x^{30}$

d)

$6x^{16}$

11.

Let x be a positive integer. If $5^4\ \cdot\ 5^x\ =\ 5^{12}\$ , what is the value of x?

a)

3

b)

8

c)

16

d)

48

12.

Write the following number in scientific notation.

205,000,000,000

a)

$2.5\ \cdot\ 10^{11}$

b)

$2.5\ \cdot\ 10^{-11}$

c)

$2.05\ \cdot\ 10^{11}$

d)

$2.05\ \cdot\ 10^{-11}$

13.

Write the following number in scientific notation.

1,320

a)

$1.32\ \cdot\ 10^1$

b)

$1.32\ \cdot\ 10^3$

c)

$1.32\ \cdot\ 10^{-1}$

d)

$1.32\ \cdot\ 10^{-3}$

14.

Write the following number in scientific notation.

0.000000041

a)

$4.1\ \cdot\ 10^{-8}$

b)

$41\ \cdot\ 10^{-9}$

c)

$4.1\ \cdot\ 10^8$

d)

$4.1\ \cdot\ 10^9$

15.

Write the following number in standard form.

$2.77\ \cdot\ 10^7$

a)

27,700,000

b)

2,770,000,000

c)

0.0000000277

d)

0.000000277

16.

Write the following number in standard form.

$5.1\ \cdot\ 10^{-2}$

a)

5,100

b)

510

c)

0.0051

d)

0.051

17.

Tell whether or not the following number is correctly written in scientific notation.

$2.038\ \cdot\ 10^{45}$

a)

Correct

b)

Incorrect

18.

Tell whether or not the following number is correctly written in scientific notation.

$18.18\ \cdot\ 10^3$

a)

Correct

b)

Incorrect

19.

Tell whether or not the following number is correctly written in scientific notation.

$9.75\ \cdot\ 8^{10}$

a)

Correct

b)

Incorrect

20.

On average, Neptune is about $2.795\ \cdot\ 10^9$ miles from the sun, whereas Earth is about 92,000,000 miles from the sun. What is the difference between Neptune’s and Earth’s distances from the sun? Write your answer in scientific notation.

a)

$2.703\ \cdot10^9$ miles

b)

$2.5714\ \cdot\ 10^{17}$ miles

c)

$2.887\ \cdot\ 10^9$ miles

d)

$30$ miles

21.

Suppose the geographic area of Alaska is $6.7\ \cdot\ 10^5$

sq. mi. and the geographic area of the Rhode Island is $1.5\ \cdot\ 10^3$ sq. mi. How many times greater is Alaska’s land area than Rhode Island’s land area? Write your answer in standard notation. Round your answer to the nearest whole number.

a)

447 times greater

b)

520 times greater

c)

4 times greater

d)

446,666,666 times greater

22.

Michael Jordan’s net worth is approximately $ $\text{}1.6\ \cdot10^9$ . Lebron James net worth is approximately $450,000,000. How much is their combined net worth?

a)

$ $1.15\ \cdot\ 10^9$

b)

$ $2.05\ \cdot\ 10^9$

c)

$ $7.2\cdot10^{17}$

d)

$ $1.645\ \cdot\ 10^9$

23.

Sue wrote $3^3\cdot\ 3^{5\ }=\ 3^{15}$ . Explain her mistake.

a)

She should have multiplied the bases together.

b)

She should have added the exponents together.

c)

She should have multiplied the bases together and added the exponents together.

d)

She didn't do anything wrong. Her answer is correct.

24.

Kyle wrote $7^3\cdot7^{2\ }=\ 49^5$ . Explain his mistake.

a)

Kyle should multiply the bases 7 x 7 and multiply the exponents 3 x 2.

b)

Kyle should keep the base of 7 and multiply the exponents 3 x 2.

c)

Kyle keep the base of 7 and add the exponents 3 + 2.

d)

Kyle should multiply the bases 7 x 7 and add the exponents 3 + 2.

25.

$\frac{\left(4x^3\right)^3}{2x^3\cdot\ 4x^3}$

a)

$0.5x^3$

b)

$0.5x$

c)

$8x^{ }$

d)

$8x^3$

Exponents & Scientific Notation - Study

Total questions: 25

Worksheet time: 2hrs 53mins

Similar Resources on Wayground