10−5=?
\( 10^{-5}=? \)
\( 7^{-4}=\text{?} \)
\( 7^5\cdot7^{-6}=\text{?} \)
\( (8\times9\times5\times3)^{-2}= \)
\( 12^4\cdot12^{-6}=\text{?} \)
First, let's recall the negative exponent rule:
We'll apply it to the expression we received:
In the final steps, we performed the exponentiation in the numerator and then wrote the answer as a decimal.
Therefore, the correct answer is option A.
We must first remind ourselves of the negative exponent rule:
When applied to given the expression we obtain the following:
Therefore, the correct answer is option C.
We begin by using the rule for multiplying exponents. (the multiplication between terms with identical bases):
We then apply it to the problem:
When in a first stage we begin by applying the aforementioned rule and then continue on to simplify the expression in the exponent,
Next, we use the negative exponent rule:
We apply it to the expression obtained in the previous step:
We then summarise the solution to the problem: Therefore, the correct answer is option B.
We begin by applying the power rule to the products within the parentheses:
That is, the power applied to a product within parentheses is applied to each of the terms when the parentheses are opened,
We apply the rule to the given problem:
Therefore, the correct answer is option c.
Note:
Whilst it could be understood that the above power rule applies only to two terms of the product within parentheses, in reality, it is also valid for the power over a multiplication of multiple terms within parentheses, as was seen in the above problem.
A good exercise is to demonstrate that if the previous property is valid for a power over a product of two terms within parentheses (as formulated above), then it is also valid for a power over several terms of the product within parentheses (for example - three terms, etc.).
We begin by using the power rule of exponents; for the multiplication of terms with identical bases:
We apply it to the given problem:
When in a first stage we apply the aforementioned rule and then simplify the subsequent expression in the exponent,
Next, we use the negative exponent rule:
We apply it to the expression that we obtained in the previous step:
Lastly we summarise the solution to the problem: Therefore, the correct answer is option A.
\( (\frac{2}{3})^{-4}=\text{?} \)
\( (3a)^{-2}=\text{?} \)
\( a\ne0 \)
\( (0.25)^{-2}=\text{?} \)
\( (-5)^{-3}=\text{?} \)
\( \frac{1}{4^{-3}}=? \)
We use the formula:
Therefore, we obtain:
We use the formula:
Therefore, we obtain:
We begin by using the negative exponent rule:
We apply it to the given expression and obtain the following:
We then use the power rule for parentheses:
We apply it to the denominator of the expression and obtain the following:
Let's summarize the solution to the problem:
Therefore, the correct answer is option A.
\( 9^{300}\cdot\frac{1}{9^{-252}}\cdot9^{-549}=\text{?} \)
\( \frac{1}{-3}\cdot3^{-4}\cdot5^3=\text{?} \)
\( 45^{-80}\cdot\frac{1}{45^{-81}}\cdot49\cdot7^{-5}=\text{?} \)
\( 4^{2x}\cdot\frac{1}{4}\cdot4^{-2}=\text{?} \)