Simplify 4¹³÷3^-5

4 answers

To simplify this expression, we can use the properties of exponents.

Recall the exponent rule: a^m / a^n = a^(m-n)

In this case, 4¹³ / 3^(-5) becomes 4^(13-(-5))

Simplifying further, 4^(13+5) = 4^18

Therefore, 4¹³ ÷ 3^(-5) simplifies to 4^18.
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To simplify 4¹³ ÷ 3^(-5), we can use the rule of exponents that states a^m ÷ a^n = a^(m-n).

4¹³ ÷ 3^(-5) = 4¹³ ÷ (1 / 3^5) = 4¹³ × 3^5.

Now, we can calculate the values of 4¹³ and 3^5:

4¹³ = 2^26 (using the fact that 4 = 2^2, so 4¹³ = (2^2)¹³ = 2^(2×13) = 2^26)

3^5 = 3 × 3 × 3 × 3 × 3 = 243.

Substituting these values back into the expression, we get:

4¹³ × 3^5 = 2^26 × 243.

At this point, it may be helpful to use a calculator to compute the final result. The exact value is an extremely large number:

2^26 × 243 ≈ 618,475,290,624 × 243 ≈ 150,094,635,296.

So, 4¹³ ÷ 3^(-5) simplifies to approximately 150,094,635,296.
wrong again