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Popular >

simplify 5*(1/5)^{n-1}

Solution

simplify

5 \cdot (\frac{1}{5})^{n - 1}

Solution

5^{- n + 2}

Solution steps

5 (\frac{1}{5})^{n - 1}

\frac{1}{5} = 5^{- 1}

= 5 (5^{- 1})^{n - 1}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(5^{- 1})^{n - 1} = 5^{- 1 \cdot (n - 1)}

= 5 \cdot 5^{- 1 \cdot (n - 1)}

Multiply:

1 \cdot (n - 1) = (n - 1)

= 5 \cdot 5^{- (n - 1)}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

5 \cdot 5^{- (n - 1)} = 5^{1 - (n - 1)}

= 5^{1 - (n - 1)}

Simplify

1 - (n - 1) : - n + 2

= 5^{- n + 2}

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Frequently Asked Questions (FAQ)

What is 5*(1/5)^{n-1} ?
The solution to 5*(1/5)^{n-1} is 5^{-n+2}