simplify 4 to the power of 13 divided by 3 to the power of negative 5
To simplify this expression, we can use the properties of exponents.
First, let's simplify 4 to the power of 13:
4^13 = 67,108,864
Next, let's simplify 3 to the power of -5:
3^-5 = 1/3^5 = 1/243
Now, we can divide 4^13 by 3^-5:
67,108,864 / (1/243) = 67,108,864 * 243 = 16,314,684,672
To simplify the expression 4^13 ÷ 3^-5, we can use the properties of exponents.
First, let's simplify 4^13. Since the base is the same (4 in this case), we can subtract the exponents when dividing. So, 4^13 is equivalent to 4^(13-0) which simplifies to 4^13.
Next, let's simplify 3^-5. A negative exponent means we need to take the reciprocal of the base. Therefore, 3^-5 is equivalent to 1/3^5.
Now we can rewrite the expression:
4^13 ÷ 3^-5 = 4^13 ÷ (1/3^5)
Since we are dividing by a fraction, we can multiply by its reciprocal:
4^13 ÷ (1/3^5) = 4^13 × (3^5/1)
Now, let's simplify further:
4^13 × (3^5/1) = (4^13 × 3^5)
To calculate the value, you can use a calculator or compute it manually.
I hope this helps!
To simplify the expression 4^13 ÷ 3^-5, you can use the rule of exponents that says a^m ÷ a^n = a^(m - n).
Step 1: Rewrite the expression using the rule of exponents:
4^13 ÷ 3^-5 = 4^13 × 3^5
Step 2: Calculate the values of 4^13 and 3^5 separately:
4^13 = 67,108,864
3^5 = 243
Step 3: Substitute the calculated values back into the expression:
67,108,864 ÷ 243
Step 4: Divide the two numbers:
67,108,864 ÷ 243 ≈ 276,824.98
Therefore, simplifying 4^13 ÷ 3^-5 gives you an approximate answer of 276,824.98.