Simple Exponents - Algebra 2

With the negative inside the parenthesis, we multiply the base four times. Since the exponent is even, our answer will be even. Answer is .

When expanding exponents, we simply multiply the base by itself for the number of times indicated by the exponential value.

When expanding exponents, we simply multiply the base by itself for the number of times indicated by the exponential value.

is expanded out to .

When we multiply the numbers, we get a product of .

First, we know that is divisible by .

Therefore:

The answer is:

First, we know is divisible by .

Therefore:

We can set-up an equation by applying the power rule of exponents.

When a number to a power is raised by an exponent, we add the exponents. Write an equation and solve for .

Simplify.

The answer is:

First, know is divisible by .

Therefore:

We can set-up an equation by applying the power rule of exponents.

When a number to a power is raised by an exponent, we add the exponents. Write an equation and solve for .

Simplify.

The answer is:

First, we know the following:

In order to figure out the whole exponent, we can apply the power rule for exponents.

We can expand to the following:

The product is:

We can expand to the following:

The product is:

To expand the exponent, we multiply the base by whatever the exponent is.

Although we have two variables, we do know that a number raised to a zero power is one. Therefore:

First, we know that is divisible by .

The conversion becomes:

First, we know that is divisible by .

The conversion becomes:

We can expand to be . Remember the negative is outside the exponent.

First multiply the first two integers:

Now multiply 36 by 6:

First multiply 6 by 6, then 3 by 6 plus the remainder.

Ones place:

Tens place:

Thus,

Now multiply 216 by 6.

Ones place:

Tens place:

Hundreds place:

Combining these results in

Substituting this back into the to be the product is then .

We can expand to be . Remember when an even number of negative values are multiplied together the product becomes positive.

First multiply the first two integers:

Now multiply 36 by -6:

First multiply 6 by 6, then 3 by 6 plus the remainder.

Ones place:

Tens place:

Thus,

Now multiply -216 by -6.

Ones place:

Tens place:

Hundreds place:

Combining these results in

The product is then .

To convert the base, we know that . Therefore . Remember to apply the power rule of exponents.

To convert the base, we know that . Therefore . Remember to apply the power rule of exponents.

We know that exponents raised to the negative power will generate fractions.

We also know that is divisible by .

However, since this a fraction, we then have the following:

.

If fractions are raised to a positive integer exponents, we know we will generate fractions; however, if a fraction is raised by a negative integer exponent, our answer will be whole number instead.

For example:

The following rule has been used in this scenario:

In this formula, is a positive exponent raising the base .

We know .

Since we are dealing with a integer and converting to fractional base, we know we need to have a negative exponent.

The answer is: