Simplify 4^13÷3^−5
.(1 point)
you sure
Apologies for the incorrect answer provided earlier. Let's simplify the expression correctly:
When we divide two powers with the same base, we subtract the exponents.
4^13 ÷ 3^(-5) = 4^13 * 3^5
To calculate the values:
4^13 = 67,108,864
3^5 = 243
Therefore, the simplified expression is:
67,108,864 * 243 = 16,314,625,792
To simplify the expression 4^13 ÷ 3^−5, we need to follow the rules of exponents.
First, we can rewrite 4^13 as (2^2)^13. This is because 4 can be expressed as 2^2.
Next, we can use the rule that states (a^m)^n is equal to a^(m*n). Applying this rule, we can simplify (2^2)^13 to 2^(2*13), which equals 2^26.
Now, we can rewrite 3^−5 as 1 / 3^5. This is because any number with a negative exponent can be written as its reciprocal with a positive exponent.
Combining the above simplifications, we have (4^13 ÷ 3^−5) = (2^26) / (1 / 3^5).
Using the rule that states a / (1/b) is equal to a * b, we can rewrite the expression as (2^26) * (3^5).
Finally, we can simplify further by applying the rule (a^m) * (a^n) is equal to a^(m+n). Therefore, (2^26) * (3^5) equals 2^(26 + 5), which is equal to 2^31.
Therefore, the simplified expression 4^13 ÷ 3^−5 is equal to 2^31.
Using the power of exponentiation rule, we can rewrite the expression as:
4^13 / 3^-5 = (4^13) * (3^5)
Now, we can calculate the values:
4^13 = 67108864
3^5 = 243
Therefore, the simplified expression is:
67108864 * 243 = 1632586752