What is (x^my^2)(2x^{m+1}y^{5-n}z) ?

The solution to (x^my^2)(2x^{m+1}y^{5-n}z) is 2zx^{2m+1}y^{-n+7}

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simplify (x^my^2)(2x^{m+1}y^{5-n}z)

simplify

(x^{m} y^{2}) (2 x^{m + 1} y^{5 - n} z)

2 z x^{2 m + 1} y^{- n + 7}

Solution steps

(x^{m} y^{2}) (2 x^{m + 1} y^{5 - n} z)

Apply exponent rule:

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

x^{m} x^{m + 1} = x^{m + m + 1}

= y^{2} \cdot 2 x^{m + m + 1} y^{5 - n} z

Add similar elements:

m + m = 2 m

= y^{2} \cdot 2 x^{2 m + 1} y^{5 - n} z

Apply exponent rule:

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

y^{2} y^{5 - n} = y^{2 + 5 - n}

= 2 x^{2 m + 1} y^{2 + 5 - n} z

Add the numbers:

2 + 5 = 7

= 2 x^{2 m + 1} y^{- n + 7} z

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5 r^{2} s^{2} (3 rs - 4 s - 2 r^{2})

- 4 (2.03)^{3} (0.9)^{- 5} (0.1)

(3 a^{2} b) \cdot (12 a^{3} b^{5})

What is (x^my^2)(2x^{m+1}y^{5-n}z) ?
The solution to (x^my^2)(2x^{m+1}y^{5-n}z) is 2zx^{2m+1}y^{-n+7}