Simplify 4^13 / 3^-5

Answer 1

To simplify the expression 4^13 / 3^-5, we can use the rules of exponents.

First, let's simplify the numerator, which is 4^13. We can rewrite this as (2^2)^13 since 4 is equal to 2^2. By the property of exponents, when we raise a power to another power, we multiply the exponents. Therefore, (2^2)^13 is equal to 2^(2*13) which simplifies to 2^26.

Next, let's simplify the denominator, which is 3^-5. To understand this expression, let's rewrite it as 1 / 3^5. By the property of exponents, when we have a negative exponent, we can move the base with the negative exponent to the denominator. Therefore, 3^-5 is equal to 1 / 3^5, which is equal to 1 / (3*3*3*3*3) or 1 / 243.

Now that we have both the numerator and the denominator simplified, we can rewrite the expression as (2^26) / (1 / 243).

To simplify a division involving fractions, we can multiply the numerator by the reciprocal of the denominator. Therefore, the expression (2^26) / (1 / 243) is equivalent to (2^26) * 243.

To multiply exponents, we add the exponents. Therefore, (2^26) * 243 is equal to 2^(26+5) * 243, which simplifies to 2^31 * 243.

Therefore, the simplified form of 4^13 / 3^-5 is 2^31 * 243.