Answer :
To solve the problem, we start with the expression
$$\left(\frac{4}{5}\right)^6.$$
When raising a fraction to a power, we apply the exponent to both the numerator and the denominator. This follows the exponent rule
$$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}.$$
Applying this rule, we have:
$$\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}.$$
Now, let's compare this with the provided options:
- Option A: $\frac{4^6}{5}$
The denominator is not raised to the power 6, so this is not equivalent.
- Option B: $\frac{4^6}{5^6}$
This exactly matches our expression.
- Option C: $6 \cdot \left(\frac{4}{5}\right)$
Multiplying by 6 does not give the same result as raising the fraction to the 6th power.
- Option D: $\frac{24}{30}$
This simplifies to $\frac{4}{5}$, which is not equal to $\left(\frac{4}{5}\right)^6$.
Thus, the expression
$$\left(\frac{4}{5}\right)^6$$
is equal to
$$\frac{4^6}{5^6},$$
which corresponds to option B.
$$\left(\frac{4}{5}\right)^6.$$
When raising a fraction to a power, we apply the exponent to both the numerator and the denominator. This follows the exponent rule
$$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}.$$
Applying this rule, we have:
$$\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}.$$
Now, let's compare this with the provided options:
- Option A: $\frac{4^6}{5}$
The denominator is not raised to the power 6, so this is not equivalent.
- Option B: $\frac{4^6}{5^6}$
This exactly matches our expression.
- Option C: $6 \cdot \left(\frac{4}{5}\right)$
Multiplying by 6 does not give the same result as raising the fraction to the 6th power.
- Option D: $\frac{24}{30}$
This simplifies to $\frac{4}{5}$, which is not equal to $\left(\frac{4}{5}\right)^6$.
Thus, the expression
$$\left(\frac{4}{5}\right)^6$$
is equal to
$$\frac{4^6}{5^6},$$
which corresponds to option B.
