Simplify 4^13÷3^-5?
To simplify this expression, we can use the properties of exponents.
First, we know that when dividing exponential expressions with the same base, we subtract the exponents. So the expression becomes:
4^13 ÷ 3^(-5) = 4^13 * 3^5
Next, we can use the rule that when multiplying exponential expressions with the same base, we add the exponents. So the expression becomes:
4^13 * 3^5 = 4^13 * 3^5 = 4^13 * (3^3 * 3^2)
Now, we can multiply the exponents:
4^13 * (3^3 * 3^2) = 4^13 * 3^5 = 4^13 * 3^(3+2)
Finally, we can simplify further by multiplying the base 4 with an exponent of 13 and the base 3 with an exponent of 5:
4^13 * 3^(3+2) = 4^13 * 3^5 = 67108864 * 243
So, the simplified expression is 67108864 * 243 or 16,285,859,072.
To simplify 4^13 ÷ 3^(-5), we can rewrite it using the properties of exponents.
First, we have 4^13 divided by 3^(-5).
We know that any number raised to the power of -n is the reciprocal of that number raised to the power of n.
So, we can rewrite 3^(-5) as 1 / 3^5.
Now, we have 4^13 ÷ (1 / 3^5).
To divide by a fraction, we multiply by its reciprocal.
So, we can rewrite the expression as 4^13 x (3^5 / 1).
Now, we can simplify the exponents.
4^13 is equal to (2^2)^13, which is equal to 2^(2 x 13), or 2^26.
3^5 is equal to 243.
So now, we have 2^26 x 243 / 1.
multiplying 2^26 and 243, we have 67,108,864 x 243.
Multiplying these two numbers together gives us the final answer, which is 16,289,938,432.
Therefore, 4^13 ÷ 3^(-5) simplifies to 16,289,938,432.
To simplify the expression 4^13 ÷ 3^-5, we need to apply the rules of exponents.
First, let's evaluate the terms separately:
4^13 = 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 = 67,108,864.
3^-5 = 1 ÷ 3^5 = 1 ÷ (3 × 3 × 3 × 3 × 3) = 1 ÷ 243 = 0.004115.
Next, substitute these values back into the expression:
67,108,864 ÷ 0.004115.
To divide by a decimal, it is easier to multiply by the reciprocal. So, we can rewrite the expression as:
67,108,864 × (1 ÷ 0.004115).
Evaluating the expression in parentheses:
1 ÷ 0.004115 = 242.699502.
Now, substitute this value back into the expression:
67,108,864 × 242.699502.
Multiplying these two values:
67,108,864 × 242.699502 = 16,278,444,181.037569.
Therefore, the simplified value of 4^13 ÷ 3^-5 is approximately 16,278,444,181.037569.