Apply the product rule of integer exponents to find the numerical equivalent of 12^−5⋅12^7. Show your work and explain how you used the product rule of integer exponents.
The product rule of integer exponents states that when multiplying two powers with the same base, you add their exponents. In this case, we have 12^-5 multiplied by 12^7.
To find the numerical value, we can simplify each term separately using the product rule:
12^-5 = 1/(12^5)
12^7 = 12 * 12 * 12 * 12 * 12 * 12 * 12
Now, we can calculate each term separately:
12^7 = 12 * 12 * 12 * 12 * 12 * 12 * 12 = 35,831,808
12^(-5) = 1/(12^5) = 1/(12 * 12 * 12 * 12 * 12) = 1/248,832
Finally, we multiply the two results:
12^(-5) * 12^7 = (1/248,832) * 35,831,808 = 143,165,576/248,832
So, the numerical equivalent of 12^(-5) * 12^7 is 575/1, which can also be written as 575.
To find the numerical equivalent of 12^−5⋅12^7 using the product rule of integer exponents, we need to apply the rule which states that when multiplying two terms with the same base, you add their exponents.
First, let's rewrite the expression using the product rule: 12^(-5) * 12^7.
Now, according to the product rule, we add the exponents: (-5) + 7 = 2.
So, 12^(-5) * 12^7 simplifies to 12^2.
To find the numerical value, we raise 12 to the power of 2: 12^2 = 12 * 12 = 144.
Therefore, the numerical equivalent of 12^−5⋅12^7 is 144.