Recall the rule that says a negative exponent can be rewritten as a positive exponent by taking the reciprocal of the base. So, we can rewrite 3^-5 as 1/3^5.
Now we have: 4^13 ÷ (1/3^5).
Using the rule that says division of two numbers with the same base can be done by subtracting their exponents, we can simplify this to:
4^(13-5) = 4^8.
Therefore, the simplified form of 4^13 ÷ 3^-5 is 4^8.
Simplify 4^13÷3^-5.
3 answers
Wrong
Apologies for the mistake. Let's simplify 4^13 ÷ 3^-5 correctly.
Recall that 3^-5 can be rewritten as 1/3^5.
Now we have: 4^13 ÷ (1/3^5).
Dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite the expression as: 4^13 * 3^5.
Using the rule that says multiplying two numbers with the same base can be done by adding their exponents, we simplify this to:
4^13 * 3^5 = 4^8 * 4^5 * 3^5.
Since 4^8 and 4^5 have the same base, we can simplify them by adding their exponents:
4^8 * 4^5 * 3^5 = 4^(8+5) * 3^5.
Simplifying further:
4^(8+5) * 3^5 = 4^13 * 3^5.
Therefore, the simplified form of 4^13 ÷ 3^-5 is 4^13 * 3^5.
Recall that 3^-5 can be rewritten as 1/3^5.
Now we have: 4^13 ÷ (1/3^5).
Dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite the expression as: 4^13 * 3^5.
Using the rule that says multiplying two numbers with the same base can be done by adding their exponents, we simplify this to:
4^13 * 3^5 = 4^8 * 4^5 * 3^5.
Since 4^8 and 4^5 have the same base, we can simplify them by adding their exponents:
4^8 * 4^5 * 3^5 = 4^(8+5) * 3^5.
Simplifying further:
4^(8+5) * 3^5 = 4^13 * 3^5.
Therefore, the simplified form of 4^13 ÷ 3^-5 is 4^13 * 3^5.