exponents and polynomials

Question 1

basic exponent rules, simplify to a single power of 2

2 to the third times 2
2x2x2 x 2
2x2x2x2

Answer 1

2 to the fourth power

Question 2

negative / zero exponents, which expression is equivalent to

2 to the negative 1 power/2 to the second power
2 to the negative first power to the negative second power
2 to the negative third power
add the powers together

Answer 2

1/2 to the third power

Question 3

convert scientific notation to standard form, write the number 5.2 x 10 to the negative fifth power in standard form

Answer 3

0.000052

Question 4

convert number to scientific notation, write the number 0.0032 in scientific notation

Answer 4

3.2 x 10 to the negative third

Question 5

multiply/divide in scientific notation, what is the quotient of 7.584 x 10 to the sixth power and 7.9 x 10 to the second power expressed in scientific notation

7.584 x 10 to the sixth power/7.9 x 10 to the second power
7.584/7.9 x 10 to the sixth power/10 to the second power
0.96x10 to the fourth power
(9.6x10 to the negative first power) x 10 to the fourth power
9.6 x (10 to the negative first power x 10 to the fourth power)

Answer 5

9.6 x 10 to the third power

Question 6

multiplying powers, fully simplify

x to the second power (3y to the third power)

Answer 6

3x to the second power y to the third power or 3y to the third power x to the second power

Question 7

raising powers to powers, fully simplify

(6xy to the fifth power)to the third power
(6)to the third power = 216
(x)to the third power = x to the third power
(y to the fifth power)to the third power = y to the fifteenth power

Answer 7

216x to the third power y to the fifthteenth power

Question 8

dividing powers, fully simplify using only positive exponents

125xy to the third power/5x to the third power y to the third power
125/5 = 5x25/5x1 = 25/1
x/x to the third power = x/x times x to the second power = 1/x to the second power
y to the third power/y to the third power = 1/1
25/1 x 1/x to the second power x 1/1

Answer 8

25/x to the second power

Question 9

negative exponents, select the equivalent expression

x to the negative fourth power times x to the negative fifth power/x to the negative sixth power
x to the sixth power/x to the fourth power times x to the fifth power
x to the sixth power/x to the ninth power

Answer 9

1/x to the third power

Question 10

negative exponents, write the following expression without negative exponents and without parentheses

(-5x) to the negative first power
1/(-5x) to the negative first power

Answer 10

1/-5x

Question 11

exponential rules, express the following fraction in simplest form using only positive exponents

5t to the fifth power/4(t to the fifth power) to the second power
5t to the fifth power/4 t to the tenth power

Answer 11

5t/4t to the fifth power

Question 12

rewrite polynomials in standard form

10+x to the fifth power/5+x to the third power

Answer 12

x to the fifth/5+x to the third power+10

Question 13

multiply binomials, express as trinomial

(3x+1)(3x+3)
9x to the second power plus 9x+3x+3

Answer 13

9x to the second power + 12x + 3