To raise a power to another power, we multiply the exponents. This is the power rule for exponents.
To demonstrate, let's simplify the expression by applying the power rule:
Note: The power rule for exponents is just a quicker alternative to using repeated multiplication, as follows:
Express as a base raised to a single exponent.
To raise a power to another power, we simply multiply the exponents:
$\left(0.2^5\right)^2=$
|
a
|
$0.2^{7}$ |
|
b
|
$0.2^{10}$ |
|
c
|
$0.4^{5}$ |
|
d
|
$0.4^{3}$ |
|
e
|
$0.2^{3}$ |
$\left(3^4\right)^5=$
|
a
|
$15^{9}$ |
|
b
|
$3^{5/4}$ |
|
c
|
$15^{20}$ |
|
d
|
$3^{9}$ |
|
e
|
$3^{20}$ |
Express as a base raised to a single exponent.
To raise a power to another power, we simply multiply the exponents:
$\left(6^{-2}\right)^{4}=$
|
a
|
$6^{2}$ |
|
b
|
$6^{-8}$ |
|
c
|
$6^{-2}$ |
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d
|
$6^{-24}$ |
|
e
|
$6^{8}$ |
$\left(\left(\dfrac{1}{3}\right)^{-3}\right)^{-1}=$
|
a
|
$\left(\dfrac{1}{3}\right)^{3}$ |
|
b
|
$\left(\dfrac{1}{3}\right)^{4}$ |
|
c
|
$\left(\dfrac{1}{3}\right)^{-4}$ |
|
d
|
$\left(\dfrac{1}{3}\right)^{-3}$ |
|
e
|
$\left(\dfrac{1}{3}\right)^{31}$ |
Express as a base raised to a single, positive exponent.
To raise a power to another power, we simply multiply the exponents:
To evaluate we find the reciprocal of the base and then raise that reciprocal to the same power but with the opposite sign:
$\left(5^{-3}\right)^{2}=$
|
a
|
$ 5$ |
|
b
|
$ \left(\dfrac{1}{10}\right)^{3} $ |
|
c
|
$ 10$ |
|
d
|
$ \left(\dfrac{1}{5}\right)^{6} $ |
|
e
|
$\dfrac{1}{5} $ |
$\left(\left(\dfrac{1}{5}\right)^5\right)^{-3}=$
|
a
|
$5^{2}$ |
|
b
|
$5^{15}$ |
|
c
|
$5^{8}$ |
|
d
|
$\left(\dfrac{1}{5}\right)^{15} $ |
|
e
|
$\left(\dfrac{1}{5}\right)^{8} $ |