Select the two expressions that are equivalent to
\[b^{9}\].
Choose 2 answers:
Choose 2 answers:
(Choice A)
\[\left(b^2\cdot b \right)^2\]
A
\[\left(b^2\cdot b \right)^2\]
(Choice B)
\[b\cdot9\]
B
\[b\cdot9\]
(Choice C)
\[\left(\dfrac{b^{7}}{b^4}\right)^2\]
C
\[\left(\dfrac{b^{7}}{b^4}\right)^2\]
(Choice D)
\[b^6 \cdot b^3\]
D
\[b^6 \cdot b^3\]
(Choice E)
\[\dfrac{b^{10}\cdot b^8}{b^9}\]
E
\[\dfrac{b^{10}\cdot b^8}{b^9}\]
I apologize for the confusion. You are correct again, neither choice A nor choice C is equivalent to \(b^9\).
The correct choices are:
(Choice D) \(b^6 \cdot b^3\)
(Choice E) \(\dfrac{b^{10}\cdot b^8}{b^9}\)
The two expressions that are equivalent to \(b^9\) are:
(Choice A) \(\left(b^2\cdot b \right)^2\)
(Choice D) \(b^6 \cdot b^3\)
A is wrong
I apologize for the mistake. You are correct, choice A is not equivalent to \(b^9\).
The correct choices are:
(Choice C) \(\left(\dfrac{b^{7}}{b^4}\right)^2\)
(Choice D) \(b^6 \cdot b^3\)
C is wrong too
To identify the two expressions that are equivalent to \(b^9\), we need to simplify each expression and check if they result in the same value. Let's go through each of the choices.
Choice A: \(\left(b^2 \cdot b\right)^2\)
To simplify this expression, we can use the rule that states when raising a power to another power, we multiply the exponents. So, \(\left(b^2 \cdot b\right)^2 = b^{2 \cdot 2} = b^4\). This expression is not equivalent to \(b^9\) since \(b^4\) is different.
Choice B: \(b \cdot 9\)
Simplifying this expression, we get \(b \cdot 9 = 9b\). This expression is not equivalent to \(b^9\) since \(9b\) is different.
Choice C: \(\left(\dfrac{b^7}{b^4}\right)^2\)
To simplify this expression, we can use the rule that states when dividing two powers with the same base, we subtract the exponents. So, \(\left(\dfrac{b^7}{b^4}\right)^2 = \left(b^{7-4}\right)^2 = b^3^2 = b^6\). This expression is not equivalent to \(b^9\) since \(b^6\) is different.
Choice D: \(b^6 \cdot b^3\)
To simplify this expression, we can use the rule that states when multiplying two powers with the same base, we add the exponents. So, \(b^6 \cdot b^3 = b^{6+3} = b^9\). This expression is equivalent to \(b^9\).
Choice E: \(\dfrac{b^{10} \cdot b^8}{b^9}\)
To simplify this expression, we can use the rule that states when dividing two powers with the same base, we subtract the exponents. So, \(\dfrac{b^{10} \cdot b^8}{b^9} = b^{10+8-9} = b^{9}\). This expression is also equivalent to \(b^9\).
Therefore, the two expressions that are equivalent to \(b^9\) are:
Choice D: \(b^6 \cdot b^3\)
Choice E: \(\dfrac{b^{10} \cdot b^8}{b^9}\)