Exponents - Math
Card 0 of 1544
Simplify the expression:
Simplify the expression:
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Remember that fraction exponents are the same as radicals.
A shortcut would be to express the terms as exponents and look for opportunities to cancel.
Either method, we then need to multiply to two terms.
Remember that fraction exponents are the same as radicals.
A shortcut would be to express the terms as exponents and look for opportunities to cancel.
Either method, we then need to multiply to two terms.
Convert the exponent to radical notation.
Convert the exponent to radical notation.
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Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.
Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.
Which of the following is equivalent to 
?
Which of the following is equivalent to
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By definition, a number raised to the 
power is the same as the square root of that number.
Since the square root of 64 is 8, 8 is our solution.
By definition, a number raised to the
Since the square root of 64 is 8, 8 is our solution.
Solve for 
:
Solve for
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Raise both sides of the equation to the inverse power of 
to cancel the exponent on the left hand side of the equation.
Subtract 
from both sides:
Raise both sides of the equation to the inverse power of
Subtract
Which of the following is equivalent to 
?
Which of the following is equivalent to
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By definition,
.
In our problem, 
and 
.
Then, we have 
.
By definition,
In our problem,
Then, we have
Simplify the expression:
Simplify the expression:
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Begin by distributing the exponent through the parentheses. The power rule dictates that an exponent raised to another exponent means that the two exponents are multiplied:
Any negative exponents can be converted to positive exponents in the denominator of a fraction:
The like terms can be simplified by subtracting the power of the denominator from the power of the numerator:
Begin by distributing the exponent through the parentheses. The power rule dictates that an exponent raised to another exponent means that the two exponents are multiplied:
Any negative exponents can be converted to positive exponents in the denominator of a fraction:
The like terms can be simplified by subtracting the power of the denominator from the power of the numerator:
Order the following from least to greatest:
Order the following from least to greatest:
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In order to solve this problem, each of the answer choices needs to be simplified.
Instead of simplifying completely, make all terms into a form such that they have 100 as the exponent. Then they can be easily compared.
, 
, 
, and 
.
Thus, ordering from least to greatest: 
.
In order to solve this problem, each of the answer choices needs to be simplified.
Instead of simplifying completely, make all terms into a form such that they have 100 as the exponent. Then they can be easily compared.
Thus, ordering from least to greatest:
What is the largest positive integer, 
, such that 
is a factor of 
?
What is the largest positive integer,
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. Thus, 
is equal to 16.
Solve for 
.
Solve for
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First, set up the equation: 
. Simplifying this result gives 
.
First, set up the equation:
What are the x-intercepts of this equation?
What are the x-intercepts of this equation?
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To find the x-intercepts, set the numerator equal to zero.
To find the x-intercepts, set the numerator equal to zero.
Simplify the following expression.
Simplify the following expression.
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When dividing with exponents, the exponent in the denominator is subtracted from the exponent in the numerator. For example: 
.
In our problem, each term can be treated in this manner. Remember that a negative exponent can be moved to the denominator.
Now, simplifly the numerals.
When dividing with exponents, the exponent in the denominator is subtracted from the exponent in the numerator. For example:
In our problem, each term can be treated in this manner. Remember that a negative exponent can be moved to the denominator.
Now, simplifly the numerals.
Solve for 
: 
Solve for
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Rewrite each side of the equation to only use a base 2:
The only way this equation can be true is if the exponents are equal.
So:
The 
on each side cancel, and moving the 
to the left side, we get:
Rewrite each side of the equation to only use a base 2:
The only way this equation can be true is if the exponents are equal.
So:
The
Simplify the expression:
Simplify the expression:
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First simplify the second term, and then combine the two:
First simplify the second term, and then combine the two:
Simplify the following expression.
Simplify the following expression.
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We are given: 
.
Recall that when we are multiplying exponents with the same base, we keep the base the same and add the exponents.
Thus, we have 
.
We are given:
Recall that when we are multiplying exponents with the same base, we keep the base the same and add the exponents.
Thus, we have
Simplify the following expression.
Simplify the following expression.
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Recall that when we are dividing exponents with the same base, we keep the base the same and subtract the exponents.
Thus, we have 
.
We also recall that for negative exponents,
.
Thus, 
.
Recall that when we are dividing exponents with the same base, we keep the base the same and subtract the exponents.
Thus, we have
We also recall that for negative exponents,
Thus,
Simplify the following exponent expression:
Simplify the following exponent expression:
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Begin by rearranging the terms in the numerator and denominator so that the exponents are positive:
Multiply the exponents:
Simplify:
Begin by rearranging the terms in the numerator and denominator so that the exponents are positive:
Multiply the exponents:
Simplify:
Find the 
-intercept(s) of 
.
Find the
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To find the 
-intercept, set 
in the equation and solve.
To find the
Find the 
-intercept(s) of 
.
Find the
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To find the 
-intercept(s) of 
, we need to set the numerator equal to zero.
That means 
.
The best way to solve for a funky equation like this is to graph it in your calculator and calculate the roots. The result is 
.
To find the
That means
The best way to solve for a funky equation like this is to graph it in your calculator and calculate the roots. The result is
Find the -intercept(s) of 
.
Find the
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To find the 
-intercept(s) of 
, we need to set the numerator equal to zero and solve.
First, notice that 
can be factored into 
. Now set that equal to zero: 
.
Since we have two sets in parentheses, there are two separate 
values that can cause our equation to equal zero: one where 
and one where 
.
Solve for each value:
and
.
Therefore there are two 
-interecpts: 
and 
.
To find the
First, notice that
Since we have two sets in parentheses, there are two separate
Solve for each value:
and
Therefore there are two
Find the 
-intercept(s) of 
.
Find the
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To find the 
-intercept(s) of 
, set the 
value equal to zero and solve.
To find the