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Which expression is equivalent to
?
A) β63
B) 36
C) ![\sqrt[3]{6}](/tpl/images/0644/5701/e334a.png)
D) ![(\frac{1}{6} )^3](/tpl/images/0644/5701/aea8e.png)
The equivalent of
is ![(\frac{1}{6} )^3](/tpl/images/0644/5701/aea8e.png)
Step-by-step explanation:
Given
Expression: ![6^{-3}](/tpl/images/0644/5701/9d0fd.png)
Required:
Find the Equivalent Expression
To find the equivalent of this expression, we make use of law of indices.
One of the laws of indices states that
![a^-b = \frac{1}{a^b}](/tpl/images/0644/5701/ecf3e.png)
If we apply this law to the expression above (
)
By comparison a = 6 and b = 3.
So,
becomes
= ![\frac{1}{6^3}](/tpl/images/0644/5701/72ce0.png)
Simplifying further;
= ![\frac{1}{6 * 6 * 6}](/tpl/images/0644/5701/8b76b.png)
This can also be written as
= ![\frac{1*1*1}{6 * 6 * 6}](/tpl/images/0644/5701/6f4db.png)
By splitting the above expression; we have that
= ![\frac{1}{6} * \frac{1}{6} * \frac{1}{6}](/tpl/images/0644/5701/f8467.png)
Multiplication law of indices states that;
a * a * a = aΒ³. (Because they have the same base of a)
So,
can then be written as ![(\frac{1}{6} )^3](/tpl/images/0644/5701/aea8e.png)
Hence, Β
= ![(\frac{1}{6} )^3](/tpl/images/0644/5701/aea8e.png)
So, the equivalent of
is ![(\frac{1}{6} )^3](/tpl/images/0644/5701/aea8e.png)