4^13÷3^-5
To solve this expression, we can simplify it using the properties of exponents.
First, let's simplify the numerator, which is 4^13. Since the base is the same, we can multiply the exponents:
4^13 = 4^(8+5) = (4^8)*(4^5)
Next, let's simplify each term:
4^8 = 4^(4+4) = (4^4)*(4^4) = 256 * 256 = 65,536
4^5 = 4^(4+1) = (4^4)*4 = 256 * 4 = 1,024
Now, we can substitute these results back into the original expression:
(4^13) / 3^-5 = (65,536 * 1,024) / 3^-5
Next, let's simplify the denominator, which is 3^-5. To convert a negative exponent to a positive exponent, we can move the base to the opposite side of the fraction and change the sign of the exponent:
3^-5 = 1 / (3^5)
Now, we can substitute this result back into the expression:
(65,536 * 1,024) / (1 / (3^5))
To divide by a fraction, we can multiply by its reciprocal:
(65,536 * 1,024) * (3^5 / 1)
Next, let's simplify the term within parentheses:
3^5 = 3^(3+2) = (3^3)*(3^2) = 27 * 9 = 243
Now, we can substitute this result back into the expression:
(65,536 * 1,024) * (243 / 1)
Next, let's simplify each term:
65,536 * 1,024 = 67,108,864
Now, we can substitute this result back into the expression:
67,108,864 * 243
Finally, we can multiply these two terms:
67,108,864 * 243 = 16,297,062,352
Therefore, 4^13 / 3^-5 is equal to 16,297,062,352.
Write 4^13÷3^-5 in simplest form
To write 4^13 ÷ 3^-5 in simplest form, let's follow the steps below:
First, let's rewrite the expression using positive exponents for both terms:
4^13 ÷ 3^-5 = 4^13 ÷ (1/3^5)
Next, let's simplify the denominator by moving 3^-5 to the numerator and changing its sign to positive:
4^13 ÷ (1/3^5) = 4^13 * 3^5
Now, let's calculate each term:
4^13 = (2^2)^13 = 2^(2*13) = 2^26
3^5 = 3^(3+2) = 3^3 * 3^2 = 27 * 9 = 243
Substituting these results back into the expression:
4^13 * 3^5 = 2^26 * 243
Now, let's simplify this expression by multiplying the terms:
2^26 * 243 = (2^6)^4 * 243 = (64)^4 * 243 = 16777216 * 243 = 4,084,793,088
Therefore, 4^13 ÷ 3^-5, in simplest form, is equal to 4,084,793,088.
To simplify the expression 4^13 ÷ 3^-5, we can use the rules of exponents.
First, let's rewrite the expression using positive exponents:
4^13 ÷ 3^-5 = (4^13) / (1/3^5)
Now, let's simplify each part of the expression:
4^13 = 67,108,864 (4 multiplied 13 times)
1/3^5 = 1/(1/243) = 243 (since 3^5 = 243)
Now, substitute these values back into the original expression:
(67,108,864) / (243)
To divide by a fraction, we can multiply by the reciprocal (flip the fraction):
67,108,864 * (1/243)
Finally, multiply the numerator and denominator:
67,108,864 ÷ 243 = 276,824