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how do you solve this rational exponent (25b^6)^-1.5?

Sagot :

[tex]Use:\left(a^n\right)^m=a^{n\cdot m}\ and\ (a\cdot b)^n=a^n\cdot b^n\\\\25=5^2\\\\(25b^6)^{-1.5}=\left(5^2b^6\right)^{1.5}=\left(5^2\right)^{-1.5}\cdot\left(b^6\right)^{-1.5}=5^{2\cdot(-1.5)}\cdot b^{6\cdot(-1.5)}\\\\=5^{-3}b^{-9}=\frac{1}{5^3b^9}=\boxed{\frac{1}{125b^9}}[/tex]
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