Exponents and their properties unit test using the quotient rule of exponents. What is the exponent in it in an equivalent form of seven with a small nine on top of it over seven with a small six on top of it if the base is seven, what's the answer?
To find the equivalent form of (7^9)/(7^6) with the base of 7, we can apply the quotient rule of exponents. According to this rule, when dividing two exponential expressions with the same base, you subtract the exponents.
In this case, (7^9)/(7^6) can be simplified as 7^(9-6).
Since 9 - 6 equals 3, the exponent in the equivalent form is 3.
The exponent in an equivalent form of seven with a small nine on top of it over seven with a small six on top of it, with a base of seven, can be found using the quotient rule of exponents.
According to the quotient rule, when dividing two exponential terms with the same base, you subtract the exponents. In this case, the base is seven, and the smaller exponent is on the denominator (seven with a small six on top of it).
So, the equivalent form of seven with a small nine on top of it over seven with a small six on top of it would be:
7^(9-6)
Simplifying the exponent, we have:
7^3
Since any number raised to the power of 3 is equal to itself multiplied by itself twice, we know that 7^3 is equal to:
7 * 7 * 7
So, the answer is 7 * 7 * 7, which equals 343.
To solve this problem using the quotient rule of exponents, we need to know the properties involved. The quotient rule states that when we divide two powers with the same base, we subtract their exponents.
Given the base of 7, we have an equivalent form of:
(7^9) / (7^6)
To apply the quotient rule, subtract the exponents:
7^(9-6)
Simplifying the exponent, we have:
7^3
The exponent in an equivalent form to (7^9) / (7^6) with a base of 7 is 7^3.
The final answer is 7^3, which is equal to 343.