Question

exponent (power)

base =
power =

base =
power =

condense
write the following using exponents:
a. 4·4·4·4·4·4
b. (-3)(-3)(-3)
c. (\frac{2}{5})(\frac{2}{5})(\frac{2}{5})(\frac{2}{5})(\frac{2}{5})
d. x·x·x·x
e. 5·5·y·y·y·y·y
f. 3·3·3·x·x·y·y·y·y

expand
write the following without using exponents:
a. 4^3
b. (\frac{2}{3})^5
c. (-3)^5
d. m^5
e. 3^2x^5
f. 5^4x^2y^3

Explanation:

Condense:

a.

The base is 4 and it is multiplied 6 times. So, $4\cdot4\cdot4\cdot4\cdot4\cdot4 = 4^{6}$.

b.

The base is - 3 and it is multiplied 3 times. So, $(-3)(-3)(-3)=(-3)^{3}$.

c.

The base is $\frac{2}{5}$ and it is multiplied 5 times. So, $(\frac{2}{5})(\frac{2}{5})(\frac{2}{5})(\frac{2}{5})(\frac{2}{5})=(\frac{2}{5})^{5}$.

d.

The base is $x$ and it is multiplied 4 times. So, $x\cdot x\cdot x\cdot x=x^{4}$.

e.

The base for 5 is 5 (multiplied 2 times) and the base for $y$ is $y$ (multiplied 5 times). So, $5\cdot5\cdot y\cdot y\cdot y\cdot y\cdot y = 5^{2}y^{5}$.

f.

The base for 3 is 3 (multiplied 3 times), the base for $x$ is $x$ (multiplied 2 times) and the base for $y$ is $y$ (multiplied 4 times). So, $3\cdot3\cdot3\cdot x\cdot x\cdot y\cdot y\cdot y\cdot y=3^{3}x^{2}y^{4}$.

Expand:

a.

$4^{3}=4\times4\times4 = 64$.

b.

$(\frac{2}{3})^{5}=\frac{2}{3}\times\frac{2}{3}\times\frac{2}{3}\times\frac{2}{3}\times\frac{2}{3}=\frac{32}{243}$.

c.

$(-3)^{5}=(-3)\times(-3)\times(-3)\times(-3)\times(-3)= - 243$.

d.

$m^{5}=m\times m\times m\times m\times m$.

e.

$3^{2}x^{5}=3\times3\times x\times x\times x\times x\times x = 9x^{5}$.

f.

$5^{4}x^{2}y^{3}=5\times5\times5\times5\times x\times x\times y\times y\times y=625x^{2}y^{3}$.

Answer:

Condense:

a. $4^{6}$
b. $(-3)^{3}$
c. $(\frac{2}{5})^{5}$
d. $x^{4}$
e. $5^{2}y^{5}$
f. $3^{3}x^{2}y^{4}$

Expand:

a. $4\times4\times4 = 64$
b. $\frac{2}{3}\times\frac{2}{3}\times\frac{2}{3}\times\frac{2}{3}\times\frac{2}{3}=\frac{32}{243}$
c. $(-3)\times(-3)\times(-3)\times(-3)\times(-3)= - 243$
d. $m\times m\times m\times m\times m$
e. $3\times3\times x\times x\times x\times x\times x = 9x^{5}$
f. $5\times5\times5\times5\times x\times x\times y\times y\times y=625x^{2}y^{3}$