4^13÷3^-5 SIMPLIFIED IN MULTIPLE WAYS

Answer 1

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.