Is the equation (4√8)^−24⋅(√8)^16=8^−48 true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)

Question

Is the equation (4√8)^−24⋅(√8)^16=8^−48 true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)

Responses

False, because the Negative Exponent Rule should be applied.

True, but the equation can be simplified further.

False, because the exponents should be added rather than multiplied.

True. When the bases are multiplied, the exponents are also multiplied.

Answer 1

True, when the bases are multiplied, the exponents are also multiplied. The equation is correct as it is.

Answer 2

True. When the bases are multiplied, the exponents are also multiplied. In this case, (4√8)^−24⋅(√8)^16 simplifies to (2^2√8)^−24⋅(2√8)^16, which further simplifies to 2^−48⋅2^32. Since the bases are the same, the exponents can be added: 2^(-48+32) = 2^(-16) = (1/2)^16 = 1/2^16. Finally, 1 is equal to 8^0, so 1/2^16 is equal to 8^0/2^16 = 8^(-16). Therefore, the equation is equal to 8^(-48) and is true.