If the expression 410 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses
(45)2
left parenthesis 4 superscript 5 baseline right parenthesis squared
(42)8
left parenthesis 4 squared right parenthesis superscript 8 baseline
4⋅4⋅4⋅4⋅4⋅4⋅4
4 times 4 times 4 times 4 times 4 times 4 times 4
(412)2
left parenthesis 4 superscript 10 baseline right parenthesis squared
To simplify the expression 410 using the Power Rule of Exponents, we need to expand it. Using the Power Rule, we multiply the base 4 by itself 10 times.
Therefore, the equivalent expanded expression is: 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4.
To clarify, the Power Rule of Exponents states that when you raise a power to another power, you multiply the exponents together. In this case, we have 4 raised to the power of 10.
To simplify the expression 4^10 using the Power Rule of Exponents, we multiply the exponents.
Therefore, an equivalent expanded expression would be:
4^10 = 4^2 * 4^8
Since 4^2 means 4 multiplied by itself (4 * 4) and 4^8 means 4 multiplied by itself 8 times (4 * 4 * 4 * 4 * 4 * 4 * 4 * 4), we can expand the expression further:
4^10 = (4 * 4) * (4 * 4 * 4 * 4 * 4 * 4 * 4 * 4)
Simplifying further, we can find the product:
4^10 = 16 * 65,536
Hence, an equivalent expanded expression is (4 * 4) * (4 * 4 * 4 * 4 * 4 * 4 * 4 * 4) = 16 * 65,536.