steps of simplifying 4^13÷3^−5

3 answers

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.