Using the Quotient Rule of Exponents, what is the exponent of 3 power of 9÷3 power of 7 when it is in exponential simplest form?(1 point)
The Quotient Rule of Exponents states that when you divide two powers with the same base, you subtract the exponents.
In this case, we have (9^3)/(3^7).
To use the Quotient Rule, we subtract the exponents of 3: 3 - 7 = -4.
Therefore, the exponent of 3 in the simplified form is -4.
To simplify the expression using the Quotient Rule of Exponents, we need to subtract the exponents.
The Quotient Rule states that when you divide two numbers with the same base, you subtract their exponents.
In this case, we have 3 raised to the power of 9 divided by 3 raised to the power of 7. So, we subtract the exponents:
3^9 ÷ 3^7 = 3^(9 - 7)
Simplifying further:
3^(9 - 7) = 3^2
Therefore, the exponent of 3 raised to the power of 9 divided by 3 raised to the power of 7 when in exponential simplest form is 2.
To simplify the expression using the Quotient Rule of Exponents, we need to subtract the exponents. The quotient rule states that when dividing the same base with different exponents, we subtract the exponents.
The expression is (9^3) ÷ (3^7).
Now, let's simplify it step by step:
First, we can simplify the numerator: 9^3 = 9 × 9 × 9 = 729.
Next, we simplify the denominator: 3^7 = 3 × 3 × 3 × 3 × 3 × 3 × 3 = 2187.
Now, we can rewrite the expression as 729 ÷ 2187.
To simplify this division further, we can factor out common factors from the numerator and denominator. In this case, we can divide both numbers by a common factor of 9 to get:
729 ÷ 2187 = (9 × 81) ÷ (9 × 243) = 81 ÷ 243.
Now, we can simplify 81 ÷ 243 by finding a common factor again. We can divide both numbers by 81, resulting in:
81 ÷ 243 = 1 ÷ 3 = 1/3.
Therefore, the expression (9^3) ÷ (3^7) simplifies to 1/3 when in exponential simplest form.