Question

Evaluate:

(7^–2)⁴ × (343)²

Answer 1

Let’s evaluate the expression step by step:

We are asked to evaluate:

(7^–2)⁴ × (343)²

Step 1: Simplify (7^–2)⁴

Use the property of exponents: (a^m)ⁿ = a^{m × n}

(7^–2)⁴

= 7^{–2 × 4}

= 7^–8 

Step 2: Simplify 343²

Notice that 343 = 7³, so: 

343² = (7³)²

= 7^{3 × 2}

= 7⁶

Step 3: Substitute and simplify

Now, the expression becomes 7^–8 × 7⁶

Step 4: Combine the powers of 7

Using the property of exponents, a^m × aⁿ = a^{m + n}, we get

7^{–8 + 6} = 7^–2

Thus, the simplified expression is 7^–2

This can also be written as `1/7^2 = 1/49`

So the value of the expression is `1/49`.