Question

Which exponential expression is equivalent to the one below? (7 * 2)^6

a) 7^6 * 2^6
b) 7^12
c) 2^6
d) 7^6 + 2^6

Answer 1

The exponential expression equivalent to (7 * 2)^6 is 7^6 * 2^6, following the rule that the exponent applies to both terms inside the parentheses when multiplied together.

Step-by-step explanation:

The student has asked to find which exponential expression is equivalent to the given expression (7 \times 2)^6. To solve this, we will use the rule of exponents which states that when two terms are multiplied inside a parenthesis and raised to an exponent, the exponent is distributed to both terms. This is written as (ab)^n = a^n \times b^n.

Applying this rule to our expression, we get (7 \times 2)^6 = 7^6 \times 2^6. Therefore, the equivalent exponential expression is option a) 7^6 \times 2^6.