Question

find the value of n 7^3n×49^1-n,=343

Answer 1

Answer:n = 1

Step-by-step explanation:

=>7^3n×49^1-n = 343

=>7^3n×7^2(1-n) = 7^3

=>7^3n+2-2n = 7^3

=>7^3n+2-2n = 7^3

comparing the powers, we get

=>3n+2-2n = 3

=>n = 3-2

=>n = 1

Answer 2

Concept:

Exponents are the powers that make it easier to multiply and divide consecutive integers.

The rules of exponent are:

The product rule for the exponent is (xᵃ)(xᵇ) = xᵃ ⁺ ᵇ.

The division rule for exponents is xᵃ/xᵇ = xᵃ ⁻ ᵇ.

The power rule for exponents is (xᵃ)ᵇ = xᵃᵇ.

The negative exponent rule is a⁻ⁿ = 1/aⁿ.

The zero power rule for exponents is a⁰ = 1.

Given:

The equation $7^{3n}\times 49^{1-n}=343$

Find:

The value of n.

Solution:

Consider the equation,

$7^{3n}\times 49^{1-n}=343$

Now, 49 can also be expressed as 7², and 343 can be written as 7³

Therefore,

$7^{3n}\times 7^{2(1-n)}=7^3$

The multiplication rule of exponents,

(xᵃ)(xᵇ) = xᵃ ⁺ ᵇ.

Therefore,

$7^{3n+2(1-n)}=7^3\\7^{3n+2-2n}=7^3$

Now,

3n + 2 - 2n = 3

n + 2 = 3

n = 1

Therefore, the value of n is 1.

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