Using the product role of exponents, what is an equivalent form of two with the small six on top of the 2×2 when they small three on top of the two
An equivalent form of the expression 2 with a small 6 on top and 2 with a small 3 on top is 2 raised to the power of (6+3), which simplifies to 2 to the power of 9.
To find an equivalent form of 2 raised to the power of 6 times 2 raised to the power of 3, we can use the product rule of exponents. According to the product rule, when multiplying powers with the same base, you add the exponents.
So, in this case, we add 6 and 3:
2^6 × 2^3 = 2^(6+3).
Simplifying the exponent, we get:
2^6 × 2^3 = 2^9.
Therefore, an equivalent form of 2 raised to the power of 6 times 2 raised to the power of 3 is 2 raised to the power of 9.
To find the equivalent form of \(2^{6} \times (2^{3})^{2}\), we can apply the product rule of exponents.
First, let's simplify the expression inside the parentheses. When we raise a power to another power, we multiply the exponents. So, \((2^{3})^{2}\) is equal to \(2^{3 \times 2}\), which gives us \(2^{6}\).
Now, we can rewrite the expression as \(2^{6} \times 2^{6}\), applying the product rule of exponents. According to the product rule, when multiplying two powers with the same base, we add the exponents. So, \(2^{6} \times 2^{6}\) becomes \(2^{6 + 6}\), which simplifies to \(2^{12}\).
Therefore, an equivalent form of \(2^{6} \times (2^{3})^{2}\) is \(2^{12}\).