Simplify 4¹³ ÷ 3-⁵
To simplify the expression 4¹³ ÷ 3⁻⁵, we can start by rewriting the exponents.
4¹³ ÷ 3⁻⁵ = 4¹³ ÷ (1/3⁵)
Now, simplify the expression inside the parentheses.
4¹³ ÷ (1/3⁵) = 4¹³ × 3⁵
Next, calculate the value of 4¹³ and 3⁵.
4¹³ = 67,108,864
3⁵ = 243
Finally, simplify the expression by dividing 67,108,864 by 243.
67,108,864 ÷ 243 = 276,824
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To simplify 4¹³ ÷ 3⁻⁵, we can use the rule that states a⁻ⁿ = 1 / aⁿ.
4¹³ ÷ 3⁻⁵ = 4¹³ × 3⁵
Now, let's calculate 4¹³ and 3⁵.
4¹³ = 67,108,864
3⁵ = 243
Putting it all together:
67,108,864 ÷ 243 = 276,824.
To simplify 4¹³ ÷ 3⁻⁵, let's break it down step-by-step:
Step 1: Apply the rule of exponents:
Dividing two numbers with the same base, you subtract the exponents.
So, 4¹³ ÷ 3⁻⁵ becomes 4¹³ x 3⁵.
Step 2: Calculate the value of 4¹³:
4¹³ = 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4
= 67,108,864.
Step 3: Calculate the value of 3⁵:
3⁵ = 3 x 3 x 3 x 3 x 3
= 243.
Step 4: Perform the division:
67,108,864 ÷ 243 = 276,824.
Therefore, 4¹³ ÷ 3⁻⁵ simplifies to 276,824.
To simplify the expression 4¹³ ÷ 3^-⁵, we can follow the rules of exponents.
Let's start with the numerator, 4¹³. The exponent tells us that we need to multiply 4 thirteen times. So, 4¹³ = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4.
This calculation can be time-consuming, so it is easier to use a calculator. When computed, 4¹³ equals 67,108,864.
Next, let's simplify the denominator, 3^-⁵. The negative exponent tells us that we need to take the reciprocal of the number with a positive exponent. So, 3^-⁵ equals 1 / 3^⁵.
To compute the denominator, 3^⁵, we need to multiply 3 five times: 3 * 3 * 3 * 3 * 3. This is equal to 243.
Now we can substitute our values into the expression: 4¹³ ÷ 3⁻⁵ = 67,108,864 ÷ (1 / 243).
Dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the expression as: 67,108,864 * 243.
Now, we can calculate this product using a calculator. The result is approximately equal to 16,319,040,352.
Therefore, the simplified value of 4¹³ ÷ 3^-⁵ is 16,319,040,352.