ludivina16
Answered

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Which of these choices show a pair of equivalent expressions? Check all that
apply.
A. (481)5 and 815/4
B. 67/2 and (VG)
C. 52/3 and (15)3
O D. 75/7 and (77)5

Which Of These Choices Show A Pair Of Equivalent Expressions Check All That Apply A 4815 And 8154 B 672 And VG C 523 And 153 O D 757 And 775 class=

Sagot :

Given:

The pair of expressions in the options.

To find:

The pairs which show a pair of equivalent expressions.

Solution:

Property of exponent:

[tex](\sqrt[n]{x})^m=x^{\frac{m}{n}}[/tex]

In option A,

[tex](\sqrt[4]{81})^5=81^{\frac{5}{4}}[/tex]

So, option A is correct.

In option B,

[tex]6^{\frac{7}{2}}=(\sqrt[2]{6})^7[/tex]

[tex]6^{\frac{7}{2}}=(\sqrt{6})^7[/tex]

So, option B is correct.

In option C,

[tex]5^{\frac{2}{3}}=(\sqrt[3]{5})^2[/tex]

[tex]5^{\frac{2}{3}}\neq (\sqrt{5})^3[/tex]

So, option C is incorrect.

In option D,

[tex]7^{\frac{5}{7}}=(\sqrt[7]{7})^5[/tex]

[tex]7^{\frac{5}{7}}\neq (\sqrt{7})^5[/tex]

So, option D is incorrect.

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