Question

By what number should [(-7/2)³]-³ be multiplied to obtain (-2/7)⁴.​

Answer 1

Step-by-step explanation:

let that number be X

[(-7/2)^3]^3 = (-7/2)^9

According to question,

(-7/2)^9 * x = (-2/7)^4

x = (-2/7)^4 / (-7/2)^9

x = (-2/7)^4 * (2/-7)^9

x = (-2/7)^4 * (-2/7)^9

x = (-2/7)^4+9

x = (-2/7)^13

required number = (-2/7)^13

Answer 2

Before Solving The problem Let see some Power & Exponents formula :-

→ x^1 = x

→ x^0 = 1

→ x^(-1) = 1/x

→ x^m*x^n = x^(m+n)

→ x^m/x^n = x^(m-n)

→ (x^m)^n = x^(mn)

→ (xy)^n = x^n*y^n

→ (x/y)^n = x^n/y^n

→ x^(-n) = (1/x)^n

Solution :-

Let us Assume That, we multiply [(-7/2)³]^(-3) By x , to obtain (-2/7)⁴.

So,

→ [(-7/2)³]^(-3) * x = (-2/7)⁴.

using (x^m)^n = x^(mn) in LHS now,

→ (-7/2)^[3 * (-3)] * x = (-2/7)⁴.

→ (-7/2)^(-9) * x = (-2/7)^4

using x^(-n) = (1/x)^n in LHS now,

→ 1/(-7/2)^9 * x = (-2/7)^4

→ (-2/7)^9 * x = (-2/7)^4

→ x = (-2/7)^4 ÷ (-2/7)^9

using x^m/x^n = x^(m-n) in RHS now, we get,

→ x = (-2/7)^(4 - 9)

→ x = (-2/7)^(-5)

using x^(-n) = (1/x)^n in Last, we get,

→ x = 1/(-2/7)^5

→ x = (-7/2)^5 (Ans.)