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What values of c and d make the equation true ∛(162xc y5) = 3x2y(∛6yd)
Solution:
Let us use the exponents rule to find the value of c and d.
Given: ∛(162xc y5) = 3x2y (∛6yd)
By taking cube on both sides
( ∛(162xc y5))3 = ( 3x2y(∛6yd))3
⇒ 162xc y5 = ( 3x2y)3( ∛6yd)3
By using the exponents rule (am)n = amn
⇒ 162xc y5 = 27 x6y3 × 6yd
By using the exponents rule am × an = am + n
⇒ 162xc y5 = 162 x6y3 + 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 ∛(162xc y5) = 3x2y(∛6yd)
Summary:
The values of c and d that make the equation ∛(162xc y5) = 3x2y(∛6yd) true are 6 and 2 respectively.
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