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
Express each of the following as a power with a different base.
a) \displaystyle
16
b) \displaystyle
4^3
c) \displaystyle
9^4
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}
Simplify.
\displaystyle
5^35^6
Simplify.
\displaystyle
(-2)^3(-2)^7
Simplify.
\displaystyle
\frac{5^6}{5^2}
Simplify.
\displaystyle
\frac{7^37^6}{7}
Simplify.
\displaystyle
7^32^67^22^5
Simplify.
\displaystyle
\frac{7^32^6}{7^22^5}
Simplify.
\displaystyle
(\frac{5}{7})^3(\frac{5}{7})^6
Simplify.
\displaystyle
\frac{(- \frac{2}{5})^{13}}{(- \frac{2}{5})^7}
Simplify.
\displaystyle
(3.1)^8(3.1)^2
Simplify.
\displaystyle
\frac{(0.012)^3}{0.012}
Simplify.
\displaystyle
x^2x^6
Simplify.
\displaystyle
y^3y^6
Simplify.
\displaystyle
\frac{m^6}{m^5}
Simplify.
\displaystyle
\frac{n^3n^2}{n}
Simplify.
\displaystyle
ab^7a^3b^4
Simplify.
\displaystyle
\frac{x^5y^6}{x^3y}
Simplify.
\displaystyle
2^3x^22^2x^5
Simplify.
\displaystyle
5^3y^35^3y^6
Simplify.
\displaystyle
\frac{4^4m^6}{4m}
Simplify.
\displaystyle
\frac{6^3q^5q^2}{6q^4}
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?
Simplify
\displaystyle
(4^3 \times 3^2)^2 \times (4^5 \times 3^2)^3
Simplify
\displaystyle
\frac{(2^5 \times5^2)^2}{(2^4 \times 5)^2}
Simplify
\displaystyle
(2x^3)^7
Simplify
\displaystyle
[(\frac{8}{5})^3]^4
Express each of the following numbers with the base indicated:
32^3 with a base of 2
Express each of the following numbers with the base indicated:
81^2 with a base of 9
Express each of the following numbers with the base indicated:
81^2 with a base of 3
Express each of the following numbers with the base indicated:
100^{15} with a base of 10
Simplify.
\displaystyle
(5^3)^5(5^4)^4
Simplify.
\displaystyle
(x^3)^4(x^5)^4
Simplify.
\displaystyle
(m^3)^4(2x^3)^7(m^3)^4(x^3)^7
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.
Determine an expression for the area of the square drawn on the hypotenuse.