Question

Simplify 4^13 divided by 3^-5 using the quotient rule of exponents

Answer 1

that answer is incorrect

Answer 2

To simplify the expression 4^13 divided by 3^-5 using the quotient rule of exponents, we subtract the exponent of the denominator from the exponent of the numerator.

Using the quotient rule, we have:

4^13 / 3^-5 = 4^13 * 3^5

Now, we can simplify each base raised to a power:

4^13 * 3^5 = (2^2)^13 * 3^5
= 2^(2*13) * 3^5
= 2^26 * 3^5

Now we can write this as a single exponent:

= 2^26 * 3^5
= 67,108,864 * 243

Multiplying these two numbers, we get:

= 16,293,536,352

Answer 3

Apologies for the incorrect answer. Let's correct the calculation.

Using the quotient rule of exponents, we subtract the exponent of the denominator from the exponent of the numerator.

4^13 / 3^-5 = 4^13 * 3^5

To simplify, we can evaluate each base raised to its respective exponent:

4^13 * 3^5 = 4^13 * (3^5 / 1^5)

Since any number raised to the power of 1 is itself, we can simplify the denominator:

4^13 * (3^5 / 1) = 4^13 * 3^5

Now, we can multiply the bases:

4^13 * 3^5 = (2^2)^13 * 3^5

Applying the power rule to simplify further:

= 2^(2*13) * 3^5
= 2^26 * 3^5

Now we can write this as a single exponent:

= 2^26 * 3^5

To compute this, we multiply the numbers:

= 67,108,864 * 243
= 16,323,739,392

Therefore, 4^13 / 3^-5 simplifies to 16,323,739,392.