steps of simplifying 4^13÷3^−5
To simplify the expression 4^13 ÷ 3^(-5), we can use the rules of exponents:
Step 1: Simplify the expression within each base separately.
4^13 = (2^2)^13 = 2^(2*13) = 2^26
3^(-5) = 1 / 3^5 = 1 / (3^5) = 1 / (3^5) = 1 / (3*3*3*3*3) = 1 / 243
Step 2: Substitute the simplified expressions back into the original expression.
4^13 ÷ 3^(-5) = 2^26 ÷ (1/243)
Step 3: Simplify the division by multiplying the numerator by the reciprocal of the denominator.
2^26 ÷ (1/243) = 2^26 * 243
Step 4: Simplify the multiplication by adding the exponents of the same base.
2^26 * 243 = 2^(26+5) * 243 = 2^31 * 243
The final simplified form of the expression 4^13 ÷ 3^(-5) is 2^31 * 243.
the -5 is not contained in a ()
Apologies for the confusion. The expression 4^13 ÷ 3^-5 can be simplified as follows:
Step 1: Apply the negative exponent rule by moving the negative exponent to the denominator and changing its sign.
4^13 ÷ 3^-5 = 4^13 × 3^5
Step 2: Simplify each term.
4^13 = (2^2)^13 = 2^(2×13) = 2^26
3^5 = 3 × 3 × 3 × 3 × 3 = 243
Step 3: Substitute the simplified expressions back into the original expression.
4^13 ÷ 3^-5 = 2^26 × 243
The simplified form of the expression 4^13 ÷ 3^-5 is 2^26 × 243.
To simplify the expression 4^13 ÷ 3^(-5), you can follow these steps:
Step 1: Understand the concept of negative exponents:
In algebra, a negative exponent is an indicator that the corresponding base should be in the denominator of a fraction. So, when you have an expression with 3^(-5), it means that 3 is the base and (-5) is the exponent. To use this concept, we can rewrite 3^(-5) as 1 / 3^5.
Step 2: Simplify the expression:
Now that we have converted 3^(-5) to 1 / 3^5, we can simplify the entire expression.
The expression becomes:
4^13 / (1 / 3^5)
Step 3: Simplify the denominator:
To simplify the denominator even further, evaluate 3^5. It is calculated by multiplying 3 by itself five times: 3 * 3 * 3 * 3 * 3 = 243. Therefore, 1 / 3^5 becomes 1 / 243.
Step 4: Simplify the fraction:
Now we have 4^13 / (1 / 243). A division of a fraction is equivalent to multiplying by the reciprocal of the fraction. Thus, we can rewrite the expression as 4^13 * 243.
Step 5: Calculate the exponentiation:
The expression 4^13 can be calculated by multiplying 4 by itself thirteen times:
4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 67,108,864.
Step 6: Calculate the final answer:
Multiply the result from step 5 (67,108,864) with 243:
67,108,864 * 243 = 16,297,507,872.
Therefore, 4^13 ÷ 3^(-5) simplifies to 16,297,507,872.