Simple Exponents - Algebra 2
Card 1 of 412
How many perfect squares satisfy the inequality 
?
How many perfect squares satisfy the inequality
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The smallest perfect square between 100 and 1,000 inclusive is 100 itself, since 
. The largest can be found by noting that 
; this makes 
the greatest perfect square in this range.
Since the squares of the integers from 10 to 31 all fall in this range, this makes 
perfect squares.
The smallest perfect square between 100 and 1,000 inclusive is 100 itself, since
Since the squares of the integers from 10 to 31 all fall in this range, this makes
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Simplify the following expression
Simplify the following expression
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Simplify the following expression
Simplify the following expression
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Evaluate the following expression:
Evaluate the following expression:
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Solve for x:
Solve for x:
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Solve for x:
Step 1: Represent 
exponentially with a base of 
, therefore 
Step 2: Set the exponents equal to each other and solve for x
Solve for x:
Step 1: Represent
Step 2: Set the exponents equal to each other and solve for x
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Solve for 
:
Solve for
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Rewrite 
in exponential form with a base of 
:
Solve for 
by equating exponents:
Rewrite
Solve for
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Solve for 
:
Solve for
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Represent 
in exponential form using a base of 
:
Solve for 
by equating exponents:
Represent
Solve for
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Simplify 
.
Simplify
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To solve this expression, remove the outer exponent and expand the terms.
By exponential rules, add all the powers when multiplying like terms.
The answer is: 
To solve this expression, remove the outer exponent and expand the terms.
By exponential rules, add all the powers when multiplying like terms.
The answer is:
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Solve for 
:
Solve for
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The first step in solving for x is to simplify the right side:
.
Next, we can re-express the left side as an exponential with 2 as the base.
Now set the new left side equal to the new right side.
With the bases now being the same, we can simply set the exponents equal to each other.
The first step in solving for x is to simplify the right side:
Next, we can re-express the left side as an exponential with 2 as the base.
Now set the new left side equal to the new right side.
With the bases now being the same, we can simply set the exponents equal to each other.
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Solve for 
:
Solve for
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To solve for x, we need to simplify both sides in order to make the equation simpler to solve.
can be rewritten as 
, and 
can be written as 
.
Setting the two sides equal to each other gives us
Since the bases are the same we can set the exponents equal to each other.
To solve for x, we need to simplify both sides in order to make the equation simpler to solve.
Setting the two sides equal to each other gives us
Since the bases are the same we can set the exponents equal to each other.
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Expand:
Expand:
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When we expand exponents, we simply repeat the base by the exponential value.
Therefore:
When we expand exponents, we simply repeat the base by the exponential value.
Therefore:
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Expand:
Expand:
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When we expand exponents, we simply repeat the base by the exponential value.
Therefore:
When we expand exponents, we simply repeat the base by the exponential value.
Therefore:
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Evaluate:
Evaluate:
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is expanded to 
.
We will simply multiply the values in order to get the answer:
We will simply multiply the values in order to get the answer:
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Evaluate:
Evaluate:
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is expanded to 
.
We will simply multiply the values in order to get the answer:
We will simply multiply the values in order to get the answer:
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Expand:
Expand:
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When exponents are negative, we can express them usinf the following format: 
in this formula, 
is a positive exponent and 
is the base.
We can express 
as 
, which is also the same as:
When exponents are negative, we can express them usinf the following format:
in this formula,
We can express
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Evaluate:
Evaluate:
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When exponents are negative, we can express them usinf the following format:
in this formula, is a positive exponent and is the base.
Therefore:
When exponents are negative, we can express them usinf the following format:
in this formula,
Therefore:
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Simplify:
Simplify:
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When adding exponents, we first need to factor common terms.
Let's start by factoring out the following:
Factor.
When adding exponents, we first need to factor common terms.
Let's start by factoring out the following:
Factor.
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Expand:
Expand:
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When a number is raised by an exponent, the base value is multiplied by itself the number of times that the exponential value indicates.
When a number is raised by an exponent, the base value is multiplied by itself the number of times that the exponential value indicates.
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Expand:
Expand:
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When a number is raised by an exponent, the base value is multiplied by itself the number of times that the exponential value indicates.
When a number is raised by an exponent, the base value is multiplied by itself the number of times that the exponential value indicates.
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Evaluate:
Evaluate:
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When a number is raised by an exponent, the base value is multiplied by itself the number of times that the exponential value indicates.
is expanded to 
.
The product is 
.
When a number is raised by an exponent, the base value is multiplied by itself the number of times that the exponential value indicates.
The product is
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