It doesn’t matter that the exponent in the denominator is negative. We can still use the quotient rule since the bases are the same, and subtract the exponent in the denominator from the exponent in the numerator. Let’s do an example where we could end up with a negative exponent in the final answer.

When you raise a power to a power what do you do with the exponents?

When raising a power to a power in an exponential expression, you find the new power by multiplying the two powers together. For example, in the following expression, x to the power of 3 is being raised to the power of 6, and so you would multiply 3 and 6 to find the new power.

How do you simplify exponents in the denominator?

Simplifying the fraction using quotient rule for exponents We’ll subtract the exponent in the denominator from the exponent in the numerator, keeping the base the same.

What happens when the larger exponent is in the denominator?

When the larger exponent was in the numerator, we were left with factors in the numerator. When the larger exponent was in the denominator, we were left with factors in the denominator—notice the numerator of 1. This leads to the Quotient Property for Exponents.

How do you divide fractions with different exponents with the same base?

Dividing fractions with exponents with different bases and exponents: (4/3) 3 / (1/2) 2 = 2.37 / 0.25 = 9.481 Dividing fractional exponents with same fractional exponent: a n/m / b n/m = ( a / b) n/m 3 3/2 / 2 3/2 = (3/2) 3/2 = 1.53/2 = √ ( 1.53 ) = √3.375 = 1.837

How to divide exponential expressions with the same base?

When dividing exponential expressions with the same base where the base is a nonzero real number, copy the common base then subtract the top exponent by the bottom exponent. We must suppose here that n n belong to the set of integers. Simplify the quotient of exponential expressions.

What is 3 -2/4 -3 divided by 64/9 using exponents?

When the bases and the exponents are different we have to calculate each exponent and then divide: 3 -2 / 4 -3 = 4 3 / 3 2 = 64 / 9 = 7.111 Dividing fractions with exponents with same fraction base: (4/3) 3 / (4/3) 2 = (4/3) 3-2 = (4/3) 1 = 4/3 = 1.333