How to divide exponents - ISEE Upper Level Quantitative Reasoning

Separate the fraction and apply the quotient of powers rule:

Any nonzero number raised to the power of 0 is equal to 1, so , and

Any nonzero number raised to the power of 0 is equal to 1, so . Therefore,

However, an expression with a denominator of 0 is undefined, so that is the correct choice.

Based on the quotient rule for exponents, we know that for any non-zero number and any integers and ,

.

We should separate the fraction and apply the quotient rule for exponents:

Based on the quotient rule for exponents, we know that for any non-zero number and any integers and ,

.

We also know that any non-zero number raised to the power of is .

We know that any non-zero number raised to the power of is equal to .

Now factor:

We know that any non-zero number raised to the power of is equal to .

Based on the quotient rule for exponents, we know that, for any non-zero number and any integers and ,

.

When a fraction is raised to a power, the numerator and the denominator are both raised to that power:

The power rule says that in order to raise a power to a power, we need to multiply the exponents, i.e.

,

where and are real numbers.

Simplify the following:

Let's begin by recalling that when dividing variables with similar base, we need to subtract the exponents.

To deal with the coefficients, simply treat them as a fraction and simplify.

So our answer is

When a fraction is raised to a power, the numerator and the denominator are both raised to that power:

The power rule says that in order to raise a power to a power, we need to multiply the exponents, i.e.

.

The Negative Exponent Rule says .

We know that any non-zero number raised to the power of is equal to .

When a fraction is raised to a power, the numerator and the denominator are both raised to that power. In addition, the power rule says that in order to raise a power to a power, multiply the exponents, i.e.

.

Based on the negative exponent rule we have:

Which says negative exponents in the numerator get moved to the denominator and become positive exponents. And negative exponents in the denominator get moved to the numerator and become positive exponents. So we can write:

Based on the power rule for exponents we can write:

That means; to raise a power to a power we need to multiply the exponents.So we have:

Separate the equation:

First we need to subtract the numbers in parentheses. So we can write:

We can alternatively write:

Based on the zero-exponent rule we have:

That means any non-zero number raised to the zero power is equal to . So we can write:

Based on the power rule for exponents we can write:

That means; to raise a power to a power we need to multiply the exponents. In addition based on the negative exponent rule we have:

Which says negative exponents in the numerator get moved to the denominator and become positive exponents. And negative exponents in the denominator get moved to the numerator and become positive exponents. So we can write:

When values having the same base are divided, their exponents are subtracted.

Therefore, the correct answer is

When dealing with dividing scientific notation, you can divide the like terms separately. First, divide 4.2 by 7.0. This yields 0.6. Then divide the 10s. because when you divide a term with the same base, you subtract exponents. This gives you a combined answer of . Since this is not in scientific notation, move the decimal over one place to the right so that it will be in the appropriate notation. This gives you .