Simplify four to the 13th power, divided by three to the power of negative
To simplify this expression, we can apply the properties of exponents.
Recall that when dividing two numbers with the same base, we subtract the exponents. So, we can rewrite the expression as:
4^13 ÷ 3^(-a)
To simplify this further, we need to evaluate the negative exponent. When a number is raised to a negative exponent, it is equivalent to taking the reciprocal of the number raised to the positive exponent. In other words, 3^(-a) is the same as 1/(3^a).
Therefore, the expression becomes:
4^13 ÷ (1/(3^a))
To divide by a fraction, we can multiply by its reciprocal. So, we can rewrite the expression as:
4^13 × (3^a/1)
Now, we can apply the properties of exponents:
4^13 × 3^a
This is the simplified form of the expression.
To simplify the expression (4^13) / (3^-x), we can start by using the exponent rules.
1. Let's rewrite 3^-x as (1/3)^x. This is because any negative exponent indicates the reciprocal of the base.
Now, the expression becomes (4^13) / (1/3)^x.
2. When we have a division involving exponents, we subtract the exponents of the same base. So, we subtract x from 13:
(4^13) / (1/3)^x = (4^13) / (1/3)^x = 4^13 / (1/3)^x = 4^13 / (3^-x) = 4^13 * 3^x
Thus, the simplified expression is 4^13 * 3^x.