Free Printable Exponents and Scientific Notation

1.

Write the number $0.853$ in scientific notation

a)

$0.853\times10^0$

b)

$85.3\times10^{-2}$

c)

$8.53\times10^0$

d)

$8.53\times10^{-1}$

2.

Simplify $\left(4^8\right)^2$

a)

$4^{16}$

b)

$32^2$

c)

$4^6$

d)

$4^{10}$

3.

Which list shows the numbers in order from least to greatest?

a)

$2.7\times10^{-2}$ , $2.7\times10^{-3}$ , $7.2\times10^{-3}$

b)

$2.7\times10^{-3}$ , $2.7\times10^{-2}$ , $7.2\times10^{-3}$

c)

$2.7\times10^{-3}$ , $7.2\times10^{-3}$ , $2.7\times10^{-2}$

d)

$7.2\times10^{-3}$ , $2.7\times10^{-3}$ , $2.7\times10^{-2}$

4.

Write the number $7.45\times10^3$ in standard notation

a)

0.00745

b)

7,450

c)

745

d)

74,500

5.

Evaluate $\left(-3\right)^{-4}$

a)

-81

b)

$\frac{1}{81}$

c)

$-\frac{1}{81}$

d)

81

6.

Divide. Write the quotient as a power. $\frac{8^8}{8^3}$

a)

40

b)

$8^5$

c)

$8^{11}$

d)

Cannot combine

7.

Write $\left(y\right)\left(y\right)\left(y\right)\left(y\right)$ in exponential form.

a)

$4^y$

b)

$y^5$

c)

$y^4$

d)

$y^{-4}$

8.

Simplify $\frac{9x^0y^{-6}}{z^{-7}}$

a)

$9xy^6z^7$

b)

$\frac{9y^6}{z^7}$

c)

$\frac{9z^7}{y^6}$

d)

$\frac{9}{y^6z^7}$

9.

Divide. Write the quotient as a power. $\frac{16^{10}}{17^3}$

a)

109

b)

$16^{13}$

c)

Cannot combine

d)

$16^7$

10.

Evaluate $a^0b^{-2}$ for $a=-2$ and $b=-3$

a)

$\frac{1}{9}$

b)

0

c)

$-\frac{2}{9}$

d)

-9

11.

Simplify $\frac{q^9y^{14}}{\left(qy\right)^7}$

a)

$q^2y^7$

b)

$q^9y^{14}$

c)

$q^9y^2$

d)

Cannot simplify

12.

Simplify $\left(2.2\times10^{11}\right)\div\left(1\times10^4\right)$ and write the answer in scientific notation

a)

$2.2\times10^4$

b)

22

c)

$2.2\times10^{11}$

d)

$2.2\times10^7$

13.

Simplify $\left(\frac{4x^7}{x^2y^4}\right)^2$

a)

$\frac{16}{x^7y^8}$

b)

$\frac{8x^{10}}{y^8}$

c)

$\frac{8x^9}{y^6}$

d)

$\frac{16x^{10}}{y^8}$

14.

Simplify $\left(\frac{3}{4}\right)^{-2}$

a)

$-\frac{2}{3}$

b)

$\frac{16}{9}$

c)

$\frac{9}{16}$

d)

$-2$

15.

Multiply $\left(5.6\times10^{-7}\right)\left(6.1\times10^4\right)$ and write the answer in scientific notation.

a)

$3.416\times10^{-5}$

b)

$2.87\times10^{-3}$

c)

$34.16\times10^{-28}$

d)

$3.416\times10^{-4}$

16.

Simplify $m^3\cdot y^6\cdot m^2$

a)

$m^5y^6$

b)

$\left(m\cdot y\right)^{11}$

c)

$my^6$

d)

$m^6y^6$

17.

Simplify $\frac{-3v^0s^{-2}}{k^{-8}}$

a)

$\frac{-3k^8}{s^2}$

b)

$\frac{-3}{s^2k^8}$

c)

$-3vs^2k^8$

d)

$\frac{-3s^2}{k^8}$

18.

Simplify $\frac{a^3b^8}{\left(ab\right)^2}$

a)

$a^3b^4$

b)

Cannot simplify

c)

$ab^6$

d)

$a^3b^8$

19.

Simplify $\left(\frac{3x^8}{x^4y^4}\right)^2$

a)

$\frac{6x^{10}}{y^6}$

b)

$\frac{9}{x^6y^8}$

c)

$\frac{6x^8}{y^8}$

d)

$\frac{9x^8}{y^8}$

20.

Simplify $\left(7\times10^8\right)\div\left(1\times10^5\right)$ and write the answer in scientific notation

a)

$7\times10^3$

b)

7

c)

$7\times10^5$

d)

$7\times10^8$

Exponents and Scientific Notation

Total questions: 20

Worksheet time: 2hrs 40mins

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