if the expression 4^10 was simplified using the Power Rule Of Exponents, what is an equivalent expanded expression? (1 point)
4^10 can be expanded using the Power Rule of Exponents as follows:
4^10 = (4^2)^5 = (16)^5 = 16 * 16 * 16 * 16 * 16 = 1048576
So, the equivalent expanded expression is 1048576.
The Power Rule of Exponents states that for any positive integer a and any nonzero real number x, (a^x)^y = a^(x*y).
In this case, the expression is 4^10. Using the Power Rule of Exponents, we can simplify this expression by multiplying the exponents:
4^10 = 4^(2*5)
Since 2*5 is equal to 10, the expression becomes:
4^10 = 4^10
Therefore, the equivalent expanded expression is 4^10.
To simplify the expression 4^10 using the Power Rule of exponents, we need to use the rule which states that if we raise a power to another power, we multiply the exponents.
In this case, the base is 4 and the exponent is 10, so we need to multiply the exponent of 10 with the exponent 1 of the base.
So the expanded expression is: 4^10 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4
Simplifying further, we can calculate the value: 4 * 4 = 16, then 16 * 4 = 64, and so on, ten times in total.
Thus, the equivalent expanded expression is: 4^10 = 16 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 1,048,576