Simplify 4^13÷3^−5.

Answer 1

We can simplify this expression by using the properties of exponents.

When dividing with exponents, we subtract the exponents:

4^13 ÷ 3^(-5) = 4^13 × 3^5

Next, we can rewrite 3^5 as (3^(-5))^-1 since any number raised to the -1 power is the reciprocal of the number:

4^13 × (3^(-5))^-1

Now, apply the power rule of exponents, which states that when raising a power to a power, we multiply the exponents:

4^13 × 3^(-5)(-1)

= 4^13 × 3^(-5) × 3^(-1)

= 4^13 × 3^(-6)

= 4^13/3^6.

Therefore, the simplified expression is 4^13/3^6.