Which is the simplified form of the expression (6 to the power of -2 times 6 to the power of 5) to the -3rd power?

Mathematics

2 answers:

julsineya [31]3 years ago

7 0

Answer:

B. 1/6^9

Step-by-step explanation:

6^-2 = 1/6^2

1/6^2 * 6^5 = 6^5/6^2 = 6^3

6^(3 * -3) = 6^-9= 1/6^9

mr_godi [17]3 years ago

3 0

Answer:

<h2>B) 1 over (6 to the power of 9)</h2>

Step-by-step explanation:

$\left(6^{-2}\cdot6^5\right)^{-3}\qquad\text{use}\ a^n\cdot a^n=a^{n+m}\\\\=(6^{-2+5})^{-3}=(6^3)^{-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=6^{(3)(-3)}=6^{-9}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{6^9}$

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