Use the Power Rule of Exponents to create a simplified equivalent expression of (12 times 12 times 12) times (12 times 12 times 12)
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.
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.
To simplify the expression using the Power Rule of Exponents, we can add the exponents when multiplying the same base.
Step 1: Simplify the expression inside the parentheses on the left side: (12 x 12 x 12) = 12^3
Step 2: Simplify the expression inside the parentheses on the right side: (12 x 12 x 12) = 12^3
Step 3: Multiply the two simplified expressions together: (12^3) * (12^3)
Step 4: Apply the Power Rule of Exponents: When multiplying two exponents with the same base, we add the exponents.
12^3 * 12^3 = 12^(3+3) = 12^6
Therefore, the simplified equivalent expression is 12^6.
To simplify the expression (12^3) * (12^3) using the Power Rule of Exponents, we need to multiply the bases and add the exponents.
First, let's simplify 12^3. This means multiplying 12 by itself three times.
12 * 12 * 12 = 1728
Now, since we have two expressions (12^3), we need to multiply them together.
1728 * 1728 = 2985984
So, the simplified equivalent expression of (12^3) * (12^3) is 2,985,984.