Using the power rule of exponents, we know that for any number a raised to the power of m, and multiplied by a raised to the power of n, we can simplify the expression by adding the exponents.
In this case, we have:
(12^3) * (12^3)
The power rule of exponents states that when multiplying two numbers with the same base, we can add the exponents:
(12^3) * (12^3) = 12^(3 + 3) = 12^6
Therefore, the simplified equivalent expression is 12^6.
Use the Power Rule of Exponents to create a simplified equivalent expression of (12 times 12 times 12) times (12 times 12 times 12)
3 answers
What exponent would make the two expressions equivalent (16^x)^6 = (16^18)?
To find the exponent, we can set the exponents inside the parentheses equal to each other.
(16^x)^6 = (16^18)
We can simplify the left side by applying the power rule of exponents. When raising a power to another power, we multiply the exponents:
16^(6x) = 16^18
Now we have the same base (16) on both sides of the equation. In order for the two expressions to be equal, the exponents must be equal as well:
6x = 18
To isolate x, we divide both sides by 6:
6x / 6 = 18 / 6
x = 3
Therefore, the exponent that would make the two expressions equivalent is x = 3.
(16^x)^6 = (16^18)
We can simplify the left side by applying the power rule of exponents. When raising a power to another power, we multiply the exponents:
16^(6x) = 16^18
Now we have the same base (16) on both sides of the equation. In order for the two expressions to be equal, the exponents must be equal as well:
6x = 18
To isolate x, we divide both sides by 6:
6x / 6 = 18 / 6
x = 3
Therefore, the exponent that would make the two expressions equivalent is x = 3.
2 answers