If `h^((2)/(3))=k^(2)`, then in terms of k, what is the value of `h^(2)`?

Options

A. `k^((2)/(3))`
B. `k^((4)/(9))`
C. `k^(3)`
D. `k^(6)`

Answer

To solve the equation \( h^{\frac{2}{3}} = k^2 \) and find the value of \( h^2 \) in terms of \( k \), we can follow these steps:

### Step 1: Start with the given equation
We have the equation:
\[ h^{\frac{2}{3}} = k^2 \]

### Step 2: Raise both sides to the power of 3
To eliminate the fractional exponent, we can raise both sides of the equation to the power of 3:
\[ (h^{\frac{2}{3}})^3 = (k^2)^3 \]

### Step 3: Simplify the left side
Using the property of exponents \( (a^m)^n = a^{m \cdot n} \), we simplify the left side:
\[ h^{\frac{2}{3} \cdot 3} = k^{2 \cdot 3} \]
This simplifies to:
\[ h^2 = k^6 \]

### Step 4: Write the final answer
Thus, we have found that:
\[ h^2 = k^6 \]

### Conclusion
The value of \( h^2 \) in terms of \( k \) is \( k^6 \).

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