13^12 ÷ 13^-10
To divide two exponents with the same base, you subtract the exponents. Therefore, 13^12 ÷ 13^-10 is equal to 13^(12 - (-10)) which is equal to 13^22.
4^13 ÷ 3^-5
To divide two exponents with the same base, you subtract the exponents. Therefore, 4^13 ÷ 3^-5 is equal to 4^13 * 3^5.
simplify 4^13 ÷ 3^-5
To simplify 4^13 ÷ 3^-5, we can rewrite it as 4^13 * 3^5.
Now, let's evaluate these exponentials separately:
4^13 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4, which is a product of four 4's repeated thirteen times.
3^5 = 3 * 3 * 3 * 3 * 3, which is a product of five 3's.
Multiplying these values together, we get:
4^13 * 3^5 = (4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4) * (3 * 3 * 3 * 3 * 3)
= 671,088,664 * 243
= 162,759,322,152
Therefore, 4^13 ÷ 3^-5 simplifies to 162,759,322,152.
apply the quotient rule of integer exponents to simplify 23^65 ÷ 23^32
According to the quotient rule of exponents, when dividing two powers with the same base, you subtract the exponents.
Therefore, 23^65 ÷ 23^32 can be simplified as 23^(65 - 32) = 23^33.
simplify this expression using the quotient rule of integer exponents 12^53 ÷ 7^53
According to the quotient rule of exponents, when dividing two powers with the same base, you subtract the exponents.
Therefore, 12^53 ÷ 7^53 can be simplified as 12^53-53 = 12^0.
Any number raised to the power of 0 is equal to 1. Therefore, 12^0 simplifies to 1.
So, 12^53 ÷ 7^53 simplifies to 1.
simplify this expression using the quotient rule of integer exponents 12^53 ÷ 7^53
a. 12^53 ÷ 7^53
b. 5^106
c. 12^106
d. 5^53