Simplify 13 to the power of 12 divided by 13 to the power of -10
When we divide two numbers with the same base, we subtract the exponents. Using this rule, we can simplify 13 to the power of 12 divided by 13 to the power of -10 as:
13^12 / 13^-10
Since the base is the same (13), we can subtract the exponents:
13^(12-(-10))
When we subtract a negative exponent, it becomes positive:
13^(12+10)
Simplifying the exponent:
13^22
To simplify 13 to the power of 12 divided by 13 to the power of -10, we can use the property of exponents that states:
a^m / a^n = a^(m - n), where "a" is a non-zero number and "m" and "n" are any real numbers.
In this case, we have 13^12 / 13^(-10). Applying the exponent property, we subtract the exponents:
13^12 / 13^(-10) = 13^(12 - (-10))
Simplifying the subtraction, we have:
13^12 / 13^(-10) = 13^(12 + 10)
Adding the exponents, we get:
13^12 / 13^(-10) = 13^22
So, 13 to the power of 12 divided by 13 to the power of -10 is equal to 13 to the power of 22.