Use the Power Rule of Exponents to simplify the expression (6^2)^4.
To simplify the expression (6^2)^4 using the Power Rule of Exponents, we multiply the exponents.
Starting with (6^2)^4, we have:
(6^2)^4 = 6^(2 * 4)
Now, we multiply 2 and 4 to get 8:
= 6^8
Therefore, the simplified expression is 6^8.
Use the Power Rule of Exponents to simplify the expression (73^4)^5
To simplify the expression (73^4)^5 using the Power Rule of Exponents, we multiply the exponents.
Starting with (73^4)^5, we have:
(73^4)^5 = 73^(4 * 5)
Now, we multiply 4 and 5 to get 20:
= 73^20
Therefore, the simplified expression is 73^20.
Use the Power Rule of Exponents to simplify the expression (78^8)^6.
To simplify the expression (78^8)^6 using the Power Rule of Exponents, we multiply the exponents.
Starting with (78^8)^6, we have:
(78^8)^6 = 78^(8 * 6)
Now, we multiply 8 and 6 to get 48:
= 78^48
Therefore, the simplified expression is 78^48.
Use the Power Rule of Exponents to create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12)
To simplify the expression (12⋅12⋅12)⋅(12⋅12⋅12) using the Power Rule of Exponents, we can rewrite it as (12^3)⋅(12^3).
Applying the Power Rule of Exponents, we multiply the exponents:
(12^3)⋅(12^3) = 12^(3+3)
Simplifying the exponent, we have:
= 12^6
Therefore, the simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12) is 12^6.
What exponent would make the two expressions equivalent: (16^x)^6=(16^18)?
To determine the exponent that would make the two expressions equivalent, we set the exponents equal to each other:
(16^x)^6 = 16^18
We need to find a value for x that satisfies this equation.
Applying the Power Rule of Exponents, we multiply the exponents:
16^(x*6) = 16^18
Therefore, we have x * 6 = 18.
To solve for x, we divide both sides of the equation by 6:
x = 18 / 6
Simplifying, we get:
x = 3
Therefore, an exponent of 3 would make the two expressions equivalent: (16^3)^6 = (16^18).