Mid Chapter Review
Chapter
Chapter 2
Section
Mid Chapter Review
Solutions 40 Videos

Express each of the following as a power with single exponent.

a) \displaystyle (7^3)^5 

b) \displaystyle (x^4)^6 

c) \displaystyle (x^3)^2 

Q1

Express each of the following as a power with a different base.

a) \displaystyle 16 

b) \displaystyle 4^3 

c) \displaystyle 9^4 

Q2

Express each of the following as a power with a single exponent.

\displaystyle \begin{array}{llllll} &(a) \phantom{.} (3^4)^2 &&(c) \phantom{.} (2^5)^3 &&(e) \phantom{.} (x^2)^3 \\ &(b) \phantom{.} (9^4)^3 &&(d) \phantom{.} (10^6)^6 &&(f) \phantom{.} (5^2)^4 \end{array} 

Q3

Simplify.

\displaystyle 5^35^6 

Q4a

Simplify.

\displaystyle (-2)^3(-2)^7 

Q4b

Simplify.

\displaystyle \frac{5^6}{5^2} 

Q4c

Simplify.

\displaystyle \frac{7^37^6}{7} 

Q4d

Simplify.

\displaystyle 7^32^67^22^5 

Q4e

Simplify.

\displaystyle \frac{7^32^6}{7^22^5} 

Q4f

Simplify.

\displaystyle (\frac{5}{7})^3(\frac{5}{7})^6 

Q5a

Simplify.

\displaystyle \frac{(- \frac{2}{5})^{13}}{(- \frac{2}{5})^7} 

Q5b

Simplify.

\displaystyle (3.1)^8(3.1)^2 

Q5c

Simplify.

\displaystyle \frac{(0.012)^3}{0.012} 

Q5d

Simplify.

\displaystyle x^2x^6 

Q6a

Simplify.

\displaystyle y^3y^6 

Q6b

Simplify.

\displaystyle \frac{m^6}{m^5} 

Q6c

Simplify.

\displaystyle \frac{n^3n^2}{n} 

Q6d

Simplify.

\displaystyle ab^7a^3b^4 

Q6e

Simplify.

\displaystyle \frac{x^5y^6}{x^3y} 

Q6f

Simplify.

\displaystyle 2^3x^22^2x^5 

Q7a

Simplify.

\displaystyle 5^3y^35^3y^6 

Q7b

Simplify.

\displaystyle \frac{4^4m^6}{4m} 

Q7c

Simplify.

\displaystyle \frac{6^3q^5q^2}{6q^4} 

Q7d

The diameter of the Earth is about 1.3 X 104 km. The diameter of the Sun is about 1.4 \times 10^6 km. About how many “Earths” could you line up along the Sun’s diameter?

Q9

Simplify

\displaystyle (4^3 \times 3^2)^2 \times (4^5 \times 3^2)^3 

Q10a

Simplify

\displaystyle \frac{(2^5 \times5^2)^2}{(2^4 \times 5)^2} 

Q10b

Simplify

\displaystyle (2x^3)^7 

Q10c

Simplify

\displaystyle [(\frac{8}{5})^3]^4 

Q10d

Express each of the following numbers with the base indicated:

32^3 with a base of 2

Q11a

Express each of the following numbers with the base indicated:

81^2 with a base of 9

Q11b

Express each of the following numbers with the base indicated:

81^2 with a base of 3

Q11c

Express each of the following numbers with the base indicated:

100^{15} with a base of 10

Q11d

Simplify.

\displaystyle (5^3)^5(5^4)^4 

Q12a

Simplify.

\displaystyle (x^3)^4(x^5)^4 

Q12b

Simplify.

\displaystyle (m^3)^4(2x^3)^7(m^3)^4(x^3)^7 

Q12c

Simplify.

\displaystyle \frac{(m^3)^4(2x^2)^7}{2^5(m^3)^3(x^3)^2} 

The length of the side of a cube is 3^5. Express its surface area (SA) and volume (V) using powers and simplify.