Question

Select the equivalent expression.

(3^-8 • 7^3)^-2
A. 7^6/3^16
B. 21^10
C. 3^16 • 7^-6

Answer 1

`{( {3}^( - 8) {7}^(3) )}^( - 2) = {3}^(16) {7}^( - 6)`

The correct answer is C.

Answer 2

In order to simplify the given expression (3⁻⁸ₓ 7³)⁻², begin by evaluating the expression inside the parentheses. The equivalent expression is option A. 7⁶/3¹⁶.

Step-by-step explanation:

In order to simplify the given expression (3⁻⁸ₓ 7³)⁻², begin by evaluating the expression inside the parentheses.

Apply the exponent to each base within the parentheses, yielding 1/3⁸ₓ 7³.

Combine the bases with the same exponent, which is -2 in this case, resulting in 7³⁻⁸ / 3⁸.

Finally, simplify the exponents to obtain 7⁻⁵ / 3⁸.

So, the equivalent expression is 7⁶/3¹⁶, as 7⁻⁵ is equivalent to 1/7⁵.

This simplification process ensures that the expression is represented in a more condensed and comprehensible form.

The result is a fraction with 7⁶ in the numerator and 3¹⁶ in the denominator, emphasizing the importance of systematically simplifying complex mathematical expressions to facilitate clearer interpretation and analysis.

Thus, the equivalent expression is option A. 7⁶/3¹⁶, as 7⁻⁵ is equivalent to 1/7⁵.