4 The expression \( 6^{3} \) has a value of 216 . Write three more expressions with exponents that also have a value of 216.

To find three more expressions with exponents that equal 216, we can express 216 in different ways using bases and exponents. 1. **Using a different base**: We can express 216 as \( 6^3 \) or \( 2^n \) for some \( n \). 2. **Finding the prime factorization**: The prime factorization of 216 is: \[ 216 = 2^3 \times 3^3 \] This means we can use combinations of these prime factors to create expressions. Now, let's create three different expressions: 1. **Using base 2**: \[ 216 = (2^3) \times (3^3) = 6^3 \implies 216 = (2 \times 3)^3 = 6^3 \] 2. **Using base 3**: \[ 216 = 3^3 \times 2^3 = (3 \times 2)^3 = 6^3 \] 3. **Using a combination of bases**: \[ 216 = 2^3 \times 3^3 = (2 \times 3)^{3} = 6^3 \] Now, let's express 216 in terms of different bases and exponents: 1. \( 2^3 \times 3^3 \) 2. \( 6^3 \) 3. \( 216^1 \) Thus, the three expressions with exponents that also have a value of 216 are: 1. \( 2^3 \times 3^3 \) 2. \( 6^3 \) 3. \( 216^1 \)