2.02 Multiplication properties of exponents
Write the following in expanded form:
3 m^{4} \cdot 2 n^{2}
Write the following in exponential form:
a \cdot a \cdot b \cdot b
3 \cdot 3 \cdot 3 \cdot 3 \cdot y \cdot y \cdot y
- 3 \cdot c \cdot c \cdot b \cdot 5 \cdot c \cdot c \cdot a \cdot b
\left( 3 p\right) \cdot \left( 3 p\right) \cdot \left( 3 p\right)
Write the term that should go in the space to make the following statements true.
a^{3} \cdot ⬚ = a^{6}
a^3 \cdot ⬚ = a^4
3 x^{13} \cdot ⬚ = 9 x^{21}
x^{9} y^{8} \cdot ⬚ = x^{11} y^{15}
x^{16} y^6 \cdot ⬚ = x^{22} y^{13}
Simplify the following, giving your answer in exponential form:
3^{9} \cdot 3^{10}
y^{2} \cdot y^{6}
x^{4} \cdot 10 x^{3}
4 y^{5} \cdot 3 y^{2}
4 y^{3} \cdot 6 y
8 y^{9} \cdot 5 y^{7}
8 y^{4} \cdot 8 y^{3}
9 m^{2} \cdot 6 m^{2}
7 y^{3} \cdot 5 y^{4}
6 y^{7} \cdot 6 y^{5} \cdot 6 y^{3}
4 y^{8} \cdot 6 y^{6} \cdot 3 y^{3}
8 y^{3} \cdot 9 y^{4}
4 y^{2} \cdot 5 y^{4} \cdot 6 y^{8}
3 y^{7} \cdot 5 y^{8} \cdot 2 y
Simplify the following, giving your answer in exponential form:
6 b c^{4} \cdot 8 b^{6} a \cdot 0
8 m^{2} n^{4} \cdot 7 m^{6} n
8 w u v \cdot 4 u w v \cdot 7 u v w \cdot 6 u v \cdot 6 v u
Simplify the following, giving your answer in exponential form:
9 y^{9} \cdot 8 \left( - y \right)^{8} \cdot 7 y^{7}
4 y^{4} \cdot \left( - 2 y^{6} \right) \cdot 4 y^{5}
\left( - 5 y^{6} \right) \cdot \left( - 3 y^{7} \right) \cdot \left( - 4 y^{7} \right)
\left( - 9 y^{5} \right) \cdot \left( - 8 y^{9} \right)
\left( - 9 b^{4} \right) \cdot 4 b^{4}
\left( - 7 y^{5} z\right) \cdot \left( - 3 y x^{3}\right)
2 v^{2} w \cdot \left( - 5 u^{2} v^{3} \right) \cdot 3 u^{3} w^{4}
\left( - 4 y^{7} \right) \cdot \left( - 6 y^{2} \right) \cdot \left( - 4 y^{2} \right)
\left( - 8 q^{4} \right) \cdot p^{2} \cdot \left( - 7 q^{4} \right) \cdot p^{3}
Simplify the following, giving your answer in exponential form:
\left(j^{2}\right)^{5}
\left(c^{9}\right)^{2}
\left(f^{8}\right)^{6}
\left(w^{3}\right)^{4}
y^{8} \cdot \left( 3 y\right)^{5}
\left(u^{6}\right)^{3} \cdot u^{2}
\left( w^{9} v^{6}\right)^{4}
\left(k^{5}\right)^{3} \cdot \left(k^{2}\right)^{8}
6 \left(r^{6}\right)^{5} \cdot 4 \left(r^{4}\right)^{7}
\left( x^{9} y\right)^{7} \cdot \left( x y^{2}\right)^{4}
10 \left(r^{7}\right)^{5} \cdot \left( 2 r s\right)^{4}
\left(p^{5}\right)^{9} \cdot \left(q^{6}\right)^{10}
\left(p^{10}\right)^{6} \cdot \left(p^{4}\right)^{3}
\left(\left(x^{3}\right)^{4}\right)^{5}
The length of the base of a triangle is 3 c^{4} and the length of its perpendicular height is 6 c^{8}. What is the expression for the area of the triangle?
What quantity multiplied by itself results in w^{100}?
Consider \left(r^{2}\right)^{4}.
State whether the following expressions are equivalent to \left(r^{2}\right)^{4}:
r^{2} \cdot r^{4}
\left( r \cdot r\right) \cdot \left( r \cdot r \cdot r \cdot r\right)
\left( r \cdot r\right)^{4}
\left( r \cdot r\right) \cdot \left( r \cdot r\right) \cdot \left( r \cdot r\right) \cdot \left( r \cdot r\right)
r^{2} \cdot r^{2} \cdot r^{2} \cdot r^{2}
State whether the following statements are correct.
\left(r^{2}\right)^{4} = r^{2 + 4}
\left(r^{2}\right)^{4} = r^{ 2 \cdot 4}
Fill in the box to complete the rule: \left(r^{2}\right)^{4} = r^{⬚}
Consider the following terms which form a pattern: \left(x^{2}\right)^{1}, \left(x^{2}\right)^{2}, \left(x^{2}\right)^{3}, \left(x^{2}\right)^{4}, \ldots
What would the fifth term be? Fully simplify your answer.
Simplify, the following expressions:
\left( - x^{3} \right)^{4}
\left( 4 y^{4}\right)^{3}
\left( 8 y^{6}\right)^{2}
\left( 3 y^{6}\right)^{2}
\left( - 2 x^{2} \right)^{2}
\left( - 3 p^{2} \right)^{5}
\left( 2 u^{5} v^{5}\right)^{4}
\left( 2 r^{2} s\right)^{4}
Write the expression that should go in the parentheses to make the following statements true.
\left( ⬚ \right)^2 = q^{12}
\left( ⬚ \right)^3 = 27q^{12}
\left( ⬚ \right)^2 = 9p^8 q^{18}