What is (sqrt(72y^{2n)})/3 (9^0)(2y^{n+2})^{-1} ?

The solution to (sqrt(72y^{2n)})/3 (9^0)(2y^{n+2})^{-1} is (sqrt(2))/(y^2)

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simplify (sqrt(72y^{2n)})/3 (9^0)(2y^{n+2})^{-1}

simplify

\frac{72 y ^{2 n}}{3} (9^{0}) (2 y^{n + 2})^{- 1}

\frac{2}{y ^{2}}

Solution steps

\frac{72 y ^{2 n}}{3} (9^{0}) (2 y^{n + 2})^{- 1}

Apply rule:

(a) = a

(9^{0}) = 9^{0}

= \frac{72 y ^{2 n}}{3} \cdot 9^{0} (2 y^{n + 2})^{- 1}

Apply exponent rule:

a^{0} = 1, a \neq = 0

9^{0} = 1

= \frac{72 y ^{2 n}}{3} \cdot 1 \cdot (2 y^{n + 2})^{- 1}

Apply exponent rule:

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

(2 y^{n + 2})^{- 1} = \frac{1}{2 y ^{n + 2}}

= \frac{72 y ^{2 n}}{3} \cdot 1 \cdot \frac{1}{2 y ^{n + 2}}

Apply rule:

a \cdot 1 = a

= \frac{72 y ^{2 n}}{3} \cdot \frac{1}{2 y ^{n + 2}}

Cancel

\frac{72 y ^{2 n}}{3} : 22 y^{n}

= 22 y^{n} \frac{1}{2 y ^{n + 2}}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 2 y ^{n} \cdot 1}{2 y ^{n + 2}}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{2 2 y ^{n}}{2 y ^{n + 2}}

Cancel the common factor:

2

= \frac{2 y ^{n}}{y ^{n + 2}}

Simplify

\frac{y ^{n}}{y ^{n + 2}} : \frac{1}{y ^{2}}

= \frac{2}{y ^{2}}

e^{- \frac{410}{400}}

(0.5) (6.644 \cdot 1 0^{- 27}) (2697170.37928)^{2}

\frac{6}{11}

\frac{e ^{2 t}}{e ^{3 t}}

What is (sqrt(72y^{2n)})/3 (9^0)(2y^{n+2})^{-1} ?
The solution to (sqrt(72y^{2n)})/3 (9^0)(2y^{n+2})^{-1} is (sqrt(2))/(y^2)