Question

Which expression is equivalent to 6–3?

Answer 1

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Which expression is equivalent to $6^{-3}$?

A) –63

B) 36

C) $\sqrt[3]{6}$

D) $(\frac{1}{6} )^3$

Answer:

The equivalent of $6^{-3$ is $(\frac{1}{6} )^3$

Step-by-step explanation:

Given

Expression: $6^{-3}$

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

$a^-b = \frac{1}{a^b}$

If we apply this law to the expression above ($6^{-3}$)

By comparison a = 6 and b = 3.

So, $6^{-3}$ becomes

$6^{-3}$ = $\frac{1}{6^3}$

Simplifying further;

$\frac{1}{6^3}$ = $\frac{1}{6 * 6 * 6}$

This can also be written as

$\frac{1}{6^3}$ = $\frac{1*1*1}{6 * 6 * 6}$

By splitting the above expression; we have that

$\frac{1}{6^3}$ = $\frac{1}{6} * \frac{1}{6} * \frac{1}{6}$

Multiplication law of indices states that;

a * a * a = a³. (Because they have the same base of a)

So, $\frac{1}{6} * \frac{1}{6} * \frac{1}{6}$ can then be written as $(\frac{1}{6} )^3$

Hence,  $\frac{1}{6^3}$ = $(\frac{1}{6} )^3$

So, the equivalent of $6^{-3}$ is $(\frac{1}{6} )^3$