Question

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?

A)6 to the 30th power
B)1 over (6 to the power of 9)
C)6 to the power of 0
D)1 over (6 to the power of 16)

Answer 1

B. 1/6^9

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

Answer 2

B) 1 over (6 to the power of 9)

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)=(1)/(a^n)\\\\=(1)/(6^9)`