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# What values of c and d make the equation true ∛(162x^{c} y^{5}) = 3x^{2}y(∛6y^{d})

**Solution: **

Let us use the exponents rule to find the value of c and d.

Given: ∛(162x^{c} y^{5}) = 3x^{2}y (∛6y^{d})

By taking cube on both sides

( ∛(162x^{c} y^{5}))^{3} = ( 3x^{2}y(∛6y^{d}))^{3}

⇒ 162x^{c} y^{5 }= ( 3x^{2}y)^{3}( ∛6y^{d})^{3}

By using the exponents rule (a^{m})** ^{n }**= a

^{mn}

⇒ 162x^{c} y^{5 }= 27 x^{6}y^{3}** ^{ }**× 6y

^{d}

By using the exponents rule a^{m }× a^{n }= a^{m + n}

⇒ 162x^{c} y^{5 }= 162 x^{6}y^{3 + d}

By comparing the powers of the corresponding variables on both the sides we get

c= 6; 5 = 3 + d or d = 2

## What values of c and d make the equation true ∛(162x^{c} y^{5}) = 3x^{2}y(∛6y^{d})

**Summary:**

The values of c and d that make the equation ∛(162x^{c} y^{5}) = 3x^{2}y(∛6y^{d}) true are 6 and 2 respectively.

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