Power Rule of Exponents
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Pre-Algebra › Power Rule of Exponents
Solve:
Explanation
Multiply the coefficients together.
Multiply . When multiplying powers of the same base, their powers can be added.
The answer is:
Solve the following
Explanation
When you raise a power to a power, you multiply the two powers together. So,
We can also look at it like this:
Solve:
Explanation
When similar bases are multiplied, their powers can be added together.
The next step is to eliminate the negative exponent.
Remember that a value to a negative power is one over that value to its positive power. Write the following rule:
Apply this rule for .
Multiply the whole number with the numerator.
Combine to one term:
Explanation
Since both terms are multiplied, the powers of each base can be added or subtracted.
According to the rules of exponents,
Therefore, our terms can combine as follows.
Simplify the following:
None of the above
Explanation
When you raise an exponent to an additional power you need to multiply the two numbers, so you will get:
which equals
Solve:
Explanation
Solve the parentheses first.
Simplify the third and fourth terms.
Combine or add the two terms.
Explanation
First, distribute the exponent outside of the parentheses to each of the elements inside of the parentheses, including the 2.
Remember that in this case, when an exponent is raised to another power, the exponents multiply.
Now we need to mutiply that answer by the outside .
For this last step, remember that the exponents on the add.
Simplify.
Explanation
The Quotient of Powers Property states when you divide two powers with the same base, you subtract the exponents.
In this case, the exponents are 8 and 6:
Simplify:
Explanation
To simplify this, first convert the second term to a negative exponent.
Since similar bases are multiplied, their powers can be added.
Simplify:
Explanation
Recall, to distribute exponents through a polynomial, you must multiply the exponents. Thus, our expression can be simplified as follows: