simplify 4^13 / 3^-15
To simplify this expression, we can rewrite the fraction using the rule that states "when dividing two numbers with the same base, subtract the exponents."
4^13 / 3^-15 can be rewritten as 4^13 * 3^15 (since dividing by a negative exponent is equivalent to multiplying by the positive exponent).
Now, let's simplify the expression further:
4^13 * 3^15 = (2^2)^13 * (3^3)^15 = 2^26 * 3^45
Therefore, the simplified form of 4^13 / 3^-15 is 2^26 * 3^45.
To simplify the expression 4^13 / 3^-15, we can first apply the rule of exponents. When dividing two numbers with the same base, we subtract the exponents.
So, 4^13 / 3^-15 can be rewritten as (4^13) * (3^15).
Next, we can evaluate the exponents.
4^13 = 4 * 4 * 4 * ... * 4 (13 times)
= 67,108,864
3^15 = 3 * 3 * 3 * ... * 3 (15 times)
= 14,348,907
Therefore, (4^13) * (3^15) = 67,108,864 * 14,348,907.
To simplify the expression 4^13 / 3^-15, we can use the rules of exponents.
Let's start by simplifying the numerator, 4^13. This means raising the base 4 to the exponent 13.
4^13 = 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 = 67,108,864
Now let's simplify the denominator, 3^-15. This means raising the base 3 to the exponent -15. When a negative exponent is present, we can rewrite it as the reciprocal of the base raised to the positive exponent.
3^-15 = 1 / 3^15
Now we can simplify the expression by dividing the numerator by the denominator.
4^13 / 3^-15 = 67,108,864 / (1 / 3^15)
To divide by a fraction, we can multiply the numerator by the reciprocal of the denominator.
4^13 / 3^-15 = 67,108,864 * (3^15 / 1)
Next, we can simplify by multiplying the numbers and the exponents.
4^13 / 3^-15 = 67,108,864 * 3^15
Finally, we get the simplified expression:
4^13 / 3^-15 = 67,108,864 * 3^15