If the expression 4^10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression?
is the answer 4⋅4⋅4⋅4⋅4⋅4⋅4?
Yes, that is correct. The expression 4^10 can be expanded as "4 multiplied by itself 10 times." So, the equivalent expanded expression is 4⋅4⋅4⋅4⋅4⋅4⋅4⋅4⋅4⋅4.
The Power Rule of Exponents states that when you raise a power to another power, you multiply the exponents.
So, if we simplify 4^10 using the Power Rule of Exponents, the equivalent expanded expression would be 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4.
To simplify the expression 4^10 using the Power Rule of Exponents, we need to multiply the base (4) by itself 10 times.
Here's how we do it step by step:
1. Start with the base, which is 4.
2. Multiply the base by itself: 4 * 4 = 16.
3. Multiply the result by the base again: 16 * 4 = 64.
4. Repeat this process until we multiply the base 10 times:
64 * 4 = 256
256 * 4 = 1024
1024 * 4 = 4096
4096 * 4 = 16384
16384 * 4 = 65536
65536 * 4 = 262144
262144 * 4 = 1048576
1048576 * 4 = 4194304
4194304 * 4 = 16777216
So, the equivalent expanded expression using the Power Rule of Exponents is 4^10 = 16 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 16,777,216.