Show all the steps to solving 12^-5 • 12^7
To solve 12^-5 • 12^7, we can first simplify the expression using the properties of exponents.
Step 1: Simplify 12^-5
Recall that a negative exponent is equal to the reciprocal of the base raised to the positive exponent. So, we have:
12^-5 = 1/12^5
Step 2: Simplify 12^7
Since both bases are the same in the expression, we can combine the exponents. Therefore, 12^7 = 12^(7+5) = 12^12.
Step 3: Plug in the simplified values
Now that we have simplified both terms in the expression, we can plug in the simplified values:
1/12^5 • 12^12
Step 4: Simplify further if possible
To simplify further, we can rewrite 12^12 as 12^(12-5) = 12^7. So, we have:
1/12^5 • 12^7 = 1/12^5 • 12^7
Step 5: Cancel out common factors
Since 12^5 appears in both the numerator and the denominator, we can cancel them to simplify further:
1/12^5 • 12^7 = 1 • 12^(7-5) = 12^2
Step 6: Calculate the final answer
Finally, we compute 12^2 to get the final answer:
12^2 = 12 × 12 = 144
Therefore, 12^-5 • 12^7 = 144.