Question

What is the correct answer to the question in the photo

Answer 1

CORRECT QUESTION :-

★ Simplify and express the results in the positive exponents : [∛x⁴y × 1/∛xy⁷]-⁴.

GIVEN :-

• [∛x⁴y × 1/∛xy⁷]-⁴.

TO FIND :-

• Simplify and express the results in the positive exponents : [∛x⁴y × 1/∛xy⁷]-⁴.

SOLUTION :-

★ Here in the question we will use some exponent and identities such as : ⁿ√x^m = x^m/n. and (x^m yⁿ)^p = x^mp xyⁿp. so let's move towards the question.

→ [∛x⁴y × 1/∛xy⁷]-⁴.

★ By using identity :- ⁿ√x^m = x^m/n.

→ [(x⁴y)^1/3 × 1/(xy⁷)^1/3]-⁴

★ By using identity :- (x^m yⁿ)^p = x^mp xyⁿp.

→ [(x^4/3 y^1/3)/(x^1/3 y^7/3)]-⁴

★ By using identity :- aⁿ/a^m = a^n-m.

→ [(x^4/3 - 1/3)/(y^7/3 - 1/3)]-⁴

→ [(x^3/3)/(y^6/3)]-⁴

→ [x/y²]-⁴

→ (y²/x)⁴

→ y⁸/x⁴

Hence the required answer to this question is y⁸/x⁴.

Answer 2

Correct question :

$[ 3√x^4y\:1 / 3√xy^7]^4$

Answer :

$x^{4}\:/\:y^{8}$

Explanation :

→ $(x^{4×4}/{3}\:y^{4/3})\:/\:(x^{4/3}\:y^{7×4}/{3})$

→ $(x^{16/3}\:y^{4/3})\:/\:(x^{4/3}\:y^{28/3})$

→ $x^{12/3}\:/\:y^{24/3}$

→ $x^{4}\:/\:y^{8}$

♥ So, It's Done ♥ !!