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Alex787 [66]
3 years ago
9

Which expression is equivalent to (81x4y16)12 for all positive values of x and y? 40.5x4y16

Mathematics
1 answer:
IrinaVladis [17]3 years ago
4 0

Answer:

(81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8

Step-by-step explanation:

Given

(81x^4y^{16})^{\frac{1}{2}}

Required

Determine an equivalent expression

Express 81 as 9^2

(9^2x^4y^{16})^{\frac{1}{2}}

Apply law of indices

9^2^{\frac{1}{2}} * x^4^{\frac{1}{2}} * y^{16}^{\frac{1}{2}}

9^{\frac{2*1}{2}} * x^{\frac{4*1}{2}} * y^{\frac{16*1}{2}}

9^{\frac{2}{2}} * x^{\frac{4}{2}} * y^{\frac{16}{2}}

9^1 * x^2 * y^8

9 * x^2 * y^8

9 x^2 y^8

Hence:

(81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8

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