Simplify 4^13 ÷ 3^-5
To simplify the expression 4^13 ÷ 3^-5, we can use the rule of exponents that states a^(m-n) is equal to a^m ÷ a^n.
Applying this rule, we can rewrite the expression as:
4^13 ÷ 3^-5 = 4^13 ÷ (1/3^5)
Next, we can flip the fraction in the denominator to change the division into multiplication:
4^13 × (3^5/1)
Now, we can simplify the powers of 4 and 3:
4^13 = (2^2)^13 = 2^26
3^5 = 3 × 3 × 3 × 3 × 3 = 243
Substituting these values back into the expression gives us:
2^26 × 243
To simplify further, we can write 243 as 3^5:
2^26 × 3^5
To multiply these terms, we add the exponents:
2^26 × 3^5 = 2^26+5 × 3^5
2^26+5 is equivalent to 2^31:
2^31 × 3^5
So the simplified form of 4^13 ÷ 3^-5 is 2^31 × 3^5.
To simplify the expression 4^13 ÷ 3^-5, you can use the rules of exponents. Firstly, let's simplify the numerator and denominator separately.
In the numerator, we have 4^13. This means we need to multiply 4 by itself 13 times:
4^13 = 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4
Now, let's simplify the denominator, which is 3^-5. This means we need to take the reciprocal of 3^5:
3^-5 = 1 / 3^5
To complete the simplification, we divide the numerator by the denominator:
(4^13) ÷ (3^-5) = (4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4) ÷ (1 / 3^5)
To divide by a fraction, we multiply by its reciprocal:
(4^13) ÷ (3^-5) = (4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4) × (3^5 / 1)
Now, let's simplify the numerator and denominator separately:
Numerator: 4^13 = 67,108,864
Denominator: 3^5 = 243
Finally, we divide the numerator by the denominator:
(4^13) ÷ (3^-5) = 67,108,864 × (243 / 1) = 16,308,641,747,968
Therefore, the simplified form of 4^13 ÷ 3^-5 is 16,308,641,747,968.
To simplify 4^13 ÷ 3^-5, we can use the rule of exponents which states that dividing two powers with the same base subtracts their exponents.
Therefore, 4^13 ÷ 3^-5 simplifies to (4^13)(3^5).
(4^13)(3^5) = (2^2^13)(3^5) = 2^26 × 3^5.
So, 4^13 ÷ 3^-5 simplifies to 2^26 × 3^5.