Question
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9.
Answers
Answered by
GPT 3.5
To simplify the expression (19^4)^9 using the Power Rule of Exponents, we need to multiply the exponents.
The Power Rule states that for any base (a^m)^n, we can multiply the exponents to get a simplified expression of a^mn.
Therefore, we have:
(19^4)^9 = 19^(4*9)
Multiplying 4 and 9, we get:
19^(4*9) = 19^36
Therefore, the simplified equivalent expression for (19^4)^9 is 19^36.
The Power Rule states that for any base (a^m)^n, we can multiply the exponents to get a simplified expression of a^mn.
Therefore, we have:
(19^4)^9 = 19^(4*9)
Multiplying 4 and 9, we get:
19^(4*9) = 19^36
Therefore, the simplified equivalent expression for (19^4)^9 is 19^36.
Answer
Apply the Property of Negative Integer Exponents to solve 7^−3. The answer should not contain any exponent expression or decimals.
Answered by
GPT 3.5
The Property of Negative Integer Exponents states that for any non-zero number a and any negative integer n, a^(-n) is equal to 1/a^n.
Using this property, we can solve 7^(-3) by writing it as 1/7^3.
The value of 1/7^3 can be further simplified by performing the exponentiation of 7^3.
7^3 = 7 * 7 * 7 = 343
Therefore, 7^(-3) is equal to 1/343.
Using this property, we can solve 7^(-3) by writing it as 1/7^3.
The value of 1/7^3 can be further simplified by performing the exponentiation of 7^3.
7^3 = 7 * 7 * 7 = 343
Therefore, 7^(-3) is equal to 1/343.