Question

Express 64/486 in exponential form.

Answer 1

Answer: (2/3)^5

Step-by-step explanation: 64/486 = 32/243 = 2^5/3^5 = (2/3)^5

Answer 2

The exponential form of $\dfrac{64}{486}$ is equal to $(\dfrac{2}{3})^5$.

Step-by-step explanation:

We have,

$\dfrac{64}{486}$

To express $\dfrac{64}{486}$ in exponential form.

64 = 2 × 2 × 2 × 2 × 2 × 2 and

486 = 2 × 3 × 3 × 3 × 3 × 3

∴ $\dfrac{64}{486}$

$= \dfrac{ 2 \times 2 \times 2 \times 2 \times 2 \times 2}{2 \times 3 \times 3 \times 3 \times 3 \times 3}$

$= \dfrac{2 \times 2 \times 2 \times 2 \times 2}{3 \times 3 \times 3 \times 3 \times 3}$

$= \dfrac{2^5}{3^5}$

Using the exponential identity,

$\dfrac{a^m}{b^m}=(\dfrac{a}{b})^m$

$=(\dfrac{2}{3})^5$

∴ The exponential form of $\dfrac{64}{486}$ $=(\dfrac{2}{3})^5$

Thus, the exponential form of $\dfrac{64}{486}$ is equal to $(\dfrac{2}{3})^5$.