Simplify 4 13th divided by 3 -5th
To simplify the expression 4^13 / 3^-5, we can apply the rule of dividing exponents with the same base by subtracting the exponents.
4^13 / 3^-5 = 4^13 / (1/3^5) = 4^13 * (3^5/1)
Now, let's simplify each part individually:
4^13 = (2^2)^13 = 2^26
3^5 = 243
Therefore, the simplified expression is:
2^26 * 243
To simplify the expression 4^13 / 3^(-5), we can use the properties of exponents.
First, recall the property that a^(-n) is equal to 1 / a^n.
Therefore, we can rewrite the expression as:
4^13 / 3^(-5) = 4^13 / (1 / 3^5)
Next, simplify the expression in the denominator:
1 / 3^5 = 1 / (3 * 3 * 3 * 3 * 3) = 1 / 243
Now, substitute this value back into the main expression:
4^13 / (1 / 243) = 4^13 * 243
To simplify further, evaluate the exponent:
4^13 = (2^2)^13 = 2^(2*13) = 2^26
Substitute this value back into the expression:
2^26 * 243 = 243 * 2^26
Therefore, the simplified form of 4^13 / 3^(-5) is 243 * 2^26.