4^13÷3^-5 SIMPLIFIED IN MULTIPLE WAYS
To simplify the expression 4^13 ÷ 3^-5, we can follow these steps:
Firstly, recall that the rule for dividing powers with the same base is to subtract the exponents. In this case, we have 4^13 ÷ 3^-5, so using this rule, we get:
4^13 ÷ 3^-5 = 4^13 × 3^5
Secondly, simplify the powers of 4 and 3:
4^13 = (2^2)^13 = 2^(2*13) = 2^26
3^5 = 3^(1+4) = 3^1 × 3^4 = 3 × 3^4
Now substitute the simplified powers back into the expression:
4^13 × 3^5 = 2^26 × (3 × 3^4) = 2^26 × 3^5 × 3^1
Finally, use the rule for multiplying powers with the same base to add the exponents:
2^26 × 3^5 × 3^1 = 2^26 × 3^(5+1) = 2^26 × 3^6
So, the simplified expression 4^13 ÷ 3^-5 is equal to 2^26 × 3^6.
To simplify the expression 4^13 ÷ 3^-5, we can use the rules of exponents. Here are multiple ways to simplify it:
Method 1:
Recall that a negative exponent can be converted to a positive exponent by taking the reciprocal of the base. With that in mind, we can rewrite the expression as follows:
4^13 ÷ 3^-5 = 4^13 ÷ (1 ÷ 3^5)
Now, by dividing by a fraction, we can multiply by its reciprocal:
4^13 ÷ (1 ÷ 3^5) = 4^13 × (3^5 ÷ 1)
Using the rule for multiplying exponents with the same base:
4^13 × 3^5 = (4 × 3)^13
So, the simplified expression is:
(4 × 3)^13 = 12^13
Method 2:
Another approach is to apply the rule for dividing exponents with the same base:
4^13 ÷ 3^-5 = 4^(13 + 5)
Simplifying the exponent:
4^(13 + 5) = 4^18
Method 3:
We can also simplify the expression by directly applying the rules for exponents:
4^13 ÷ 3^-5
To divide by a negative exponent, we can rewrite it as a positive exponent:
4^13 × 3^5
To multiply exponents with the same base:
(4 × 3)^13
So, the simplified expressions can be written as:
Method 1: 12^13
Method 2: 4^18
Method 3: (4 × 3)^13 or 12^13