Question

Which expression is equivalent to (7³)⁻²?
a) 1/7⁶
b) 7
c) 1/7
d) -1/7⁶

Answer 1

The expression equivalent to (7³)⁻² is 1/7⁶.

Step-by-step explanation:

To find the expression equivalent to (7³)⁻², we need to simplify the exponent first. The power rule for exponents states that when raising a power to another power, you multiply the exponents. So, 7³⁻² is equal to 7^(3 * -2), which simplifies to 7⁻⁶.

The reciprocal rule for exponents states that to make a negative exponent positive, you can take the reciprocal of the base and change the sign of the exponent. So, 7⁻⁶ is equal to 1/7⁶.

Therefore, the expression equivalent to (7³)⁻² is a) 1/7⁶.