Using the quotient rule of exponents, what is the exponent of three with a small nine on top of it divided by three with a small seven on top of it when it is in exponential simplest form?
The quotient rule of exponents states that when dividing two exponential expressions with the same base, you subtract the exponents.
In this case, we have 3⁹ ÷ 3⁷.
Applying the quotient rule, we subtract the exponents: 9 - 7 = 2.
Therefore, the exponential expression 3⁹ ÷ 3⁷ simplifies to 3², which is equal to 9.
To simplify the expression with exponents using the quotient rule, we subtract the exponent in the denominator from the exponent in the numerator.
The quotient rule states that when dividing two exponential expressions with the same base, we subtract the exponents:
a^m / a^n = a^(m - n)
In this case, we have 3⁹ / 3⁷.
Applying the quotient rule, we subtract the exponent in the denominator from the exponent in the numerator:
3⁹ / 3⁷ = 3^(9 - 7) = 3²
So, the exponent of 3 with a small 9 on top of it divided by 3 with a small 7 on top of it, in exponential simplest form, is 3 squared or 3².
To simplify the exponent expression using the quotient rule of exponents, we subtract the exponent in the denominator from the exponent in the numerator.
In this case, we have:
\(3^{\frac{9}{3}} \div 3^{\frac{7}{3}}\)
Using the quotient rule of exponents, we subtract the exponents:
\(3^{\frac{9}{3} - \frac{7}{3}}\)
The numerator and denominator both have a common denominator of 3, so we can simplify the exponent further:
\(3^{\frac{2}{3}}\)
Hence, the exponential simplest form of \(3^{\frac{9}{3}} \div 3^{\frac{7}{3}}\) is \(3^{\frac{2}{3}}\).