Simplify the following:
Simplify the following:
\( \frac{a^4}{a^{-6}}= \)
\( \frac{2^4}{2^3}= \)
\( \frac{9^9}{9^3}= \)
\( \)
Insert the corresponding expression:
\( \frac{5^9}{5^9} \)
Insert the corresponding expression:
\( \frac{8^{16}}{8^8}= \)
Simplify the following:
Since a division operation between two terms with identical bases is required, we will use the power property to divide terms with identical bases:
Note that using this property is only possible when the division is performed between terms with identical bases.
We return to the problem and apply the power property:
Therefore, the correct answer is option C.
Let's keep in mind that the numerator and denominator of the fraction have terms with the same base, therefore we use the property of powers to divide between terms with the same base:
We apply it in the problem:
Remember that any number raised to the 1st power is equal to the number itself, meaning that:
Therefore, in the problem we obtain:
Therefore, the correct answer is option a.
Note that in the fraction and its denominator, there are terms with the same base, so we will use the law of exponents for division between terms with the same base:
Let's apply it to the problem:
Therefore, the correct answer is b.
Insert the corresponding expression:
To solve this problem, we apply the Power of a Quotient Rule for exponents. This rule is applicable when both the numerator and the denominator of a fraction have the same base. The rule states:
For our problem, the expression is:
In this expression, the base is , is , and is also . We apply the rule as follows:
Calculating the exponent:
So the expression becomes:
Any number raised to the power of 0 is 1, but in this context, we are simply reducing the original expression to its simplest form. Therefore, is the correct answer.
The solution to the question is:
Insert the corresponding expression:
The given expression is . To solve this, we apply the Power of a Quotient Rule for Exponents.
This rule states that when dividing two exponential expressions with the same base, we subtract the exponent of the denominator from the exponent of the numerator. Mathematically, it can be expressed as:
In this problem, the base is the same in both the numerator and the denominator, so we can apply this rule.
Subtract the exponent of the denominator from the exponent of the numerator:
Therefore, the simplified form of the given expression is:
Thus, the answer is .
Insert the corresponding expression:
\( \frac{25^9}{25^2}= \)
Insert the corresponding expression:
\( \frac{60^{60}}{60^{42}}= \)
Insert the corresponding expression:
\( \frac{13^{17}}{13^{14}}= \)
Insert the corresponding expression:
\( \frac{5^3}{5^8}= \)
Insert the corresponding expression:
\( \frac{9^{15}}{9^{10}}= \)
Insert the corresponding expression:
To solve the expression , we will use the Power of a Quotient Rule for Exponents. According to this rule, when dividing like bases, we subtract the exponents.
In the given expression, the base is the same for both the numerator and the denominator. Therefore, we can apply the rule as follows:
Identify the exponents: and .
Subtract the exponents: .
Write the result as a single power of the base: .
Thus, the expression simplifies to .
The solution to the question is: 25^7
Insert the corresponding expression:
To solve the expression , we need to apply the Power of a Quotient Rule for Exponents. This rule states that when dividing like bases, we subtract the exponents. In mathematical terms, for any non-zero number , and integers and , .
Applying this rule to our problem:
We have the same base:.
We subtract the exponent in the denominator from the exponent in the numerator: .
This simplifies the expression to .
Therefore, the solution to the question is: .
Insert the corresponding expression:
To solve the expression , we use the Power of a Quotient Rule for Exponents. This rule states that , where is a non-zero number, and and are integers.
In the given expression, , , and . Applying the power of a quotient rule, we perform the following calculation:
Subtract the exponent in the denominator from the exponent in the numerator: .
This simplification leads us to:
Therefore, the final simplified expression is .
Insert the corresponding expression:
We need to simplify the expression using the rules of exponents. Specifically, we will use the power of a quotient rule for exponents which states that when you divide like bases you subtract the exponents:
.
Here, the base is 5, the exponent in the numerator is 3, and the exponent in the denominator is 8.
Therefore, the simplified expression is .
The solution to the question is:
Insert the corresponding expression:
To solve the expression , we will use the Power of a Quotient rule for exponents, which states that . This rule applies when both the numerator and the denominator have the same base.
In our problem, both the numerator and the denominator have the base 9, hence we can apply the rule:
The solution to the question is:
\( \frac{3^5}{3^2}= \)
\( \frac{5^6}{5^4}= \)
Simplify the following:
\( \frac{a^5}{a^3}= \)
Simplify the following:
\( \frac{a^7}{a^3}= \)
Simplify the following:
\( \frac{a^3}{a^1}= \)
Using the quotient rule for exponents: .
Here, we have
Simplifying, we get
Using the quotient rule for exponents: .
Here, we have . Simplifying, we get .
Simplify the following:
Since a division operation between two terms with identical bases is required, we will use the power property to divide between terms with identical bases:
Note that using this property is only possible when the division is carried out between terms with identical bases.
We return to the problem and apply the mentioned power property:
Therefore, the correct answer is option A.
Simplify the following:
Sincw a division operation between two terms with identical bases is required, we will use the power property to divide between terms with identical bases:
Note that using this property is only possible when the division is performed between terms with identical bases.
We return to the problem and apply the power property:
Therefore, the correct answer is option C.
Simplify the following:
Since a division operation between two terms with identical bases is required, we will use the power property to divide between terms with identical bases:
Note that using this property is only possible when the division is performed between terms with identical bases.
We return to the problem and apply the power property:
Therefore, the correct answer is option A.
Choose the expression that is equal to the following:
\( a^5:a^4 \)
Simplify the following expression:
\( \frac{a^9}{a^x} \)
Solve the following exercise
\( \frac{a^{7y}}{a^{5x}} \)
Insert the corresponding expression:
\( \frac{x^7}{x^2}= \)
Insert the corresponding expression:
\( \frac{a^8}{a}= \)
Choose the expression that is equal to the following:
First, for good order, let's write the expression as a fraction:
Then we'll recall the law of exponents for division between terms with equal bases:
and we'll apply this law to our problem:
where in the second step we calculated the result of the subtraction in the exponent and then used the fact that any number raised to the power of 1 equals the number itself, meaning that:
We got that: therefore the correct answer is a.
Simplify the following expression:
In the question there is a fraction that has terms with identical bases in its numerator and denominator. Therefore, so we can use the distributive property of division to solve the exercise:
We apply the previously distributive property to the problem:
Therefore, the correct answer is (c).
Solve the following exercise
Let's consider that in the given problem there is a fraction in both the numerator and denominator with terms of identical bases. Hence we use the property of division between terms of identical bases in order to solve the exercise:
We apply the previously mentioned property to the problem:
Therefore, the correct answer is option A.
Insert the corresponding expression:
To solve the expression , we need to apply the power of a quotient rule for exponents. This rule states that , where is a nonzero number, and and are integers. This rule allows us to subtract the exponent in the denominator from the exponent in the numerator, given that the bases are the same.
Here's a step-by-step breakdown of applying the formula:
Therefore, simplifies to .
The solution to the question is: x^5
Insert the corresponding expression:
To solve the expression , we can use the Power of a Quotient Rule for Exponents. According to this rule, when dividing like bases, we subtract the exponents.
The general formula for this is:
For the given expression:
Now, applying the formula:
Therefore, the solution to the question is:
a^7